Fall 2018

Thursdays in 901 Van Vleck Hall at 2:25 PM, unless otherwise noted. We usually end for questions at 3:15 PM.

If you would like to sign up for the email list to receive seminar announcements then please send an email to join-probsem@lists.wisc.edu

Friday, August 10, 10am, B239 Van Vleck András Mészáros, Central European University, Budapest

Title: The distribution of sandpile groups of random regular graphs

Abstract: We study the distribution of the sandpile group of random [math]\displaystyle{ d }[/math]-regular graphs. For the directed model we prove that it follows the Cohen-Lenstra heuristics, that is, the probability that the [math]\displaystyle{ p }[/math]-Sylow subgroup of the sandpile group is a given [math]\displaystyle{ p }[/math]-group [math]\displaystyle{ P }[/math], is proportional to [math]\displaystyle{ |\operatorname{Aut}(P)|^{-1} }[/math]. For finitely many primes, these events get independent in limit. Similar results hold for undirected random regular graphs, there for odd primes the limiting distributions are the ones given by Clancy, Leake and Payne.

Our results extends a recent theorem of Huang saying that the adjacency matrices of random [math]\displaystyle{ d }[/math]-regular directed graphs are invertible with high probability to the undirected case.

September 20, Hao Shen, UW-Madison

Title: Stochastic quantization of Yang-Mills

Abstract: "Stochastic quantization” refers to a formulation of quantum field theory as stochastic PDEs. Interesting progress has been made these years in understanding these SPDEs, examples including Phi4 and sine-Gordon. Yang-Mills is a type of quantum field theory which has gauge symmetry, and its stochastic quantization is a Yang-Mills flow perturbed by white noise. In this talk we start by an Abelian example where we take a symmetry-preserving lattice regularization and study the continuum limit. We will then discuss non-Abelian Yang-Mills theories and introduce a symmetry-breaking smooth regularization and restore the symmetry using a notion of gauge-equivariance. With these results we can construct dynamical Wilson loop and string observables. Based on [S., arXiv:1801.04596] and [Chandra,Hairer,S., work in progress].

September 27, Timo Seppäläinen UW-Madison

Title:Random walk in random environment and the Kardar-Parisi-Zhang class

Abstract:This talk concerns a relationship between two much-studied classes of models of motion in a random medium, namely random walk in random environment (RWRE) and the Kardar-Parisi-Zhang (KPZ) universality class. Barraquand and Corwin (Columbia) discovered that in 1+1 dimensional RWRE in a dynamical beta environment the correction to the quenched large deviation principle obeys KPZ behavior. In this talk we condition the beta walk to escape at an atypical velocity and show that the resulting Doob-transformed RWRE obeys the KPZ wandering exponent 2/3. Based on joint work with Márton Balázs (Bristol) and Firas Rassoul-Agha (Utah).

October 4, Elliot Paquette, OSU

Title: Distributional approximation of the characteristic polynomial of a Gaussian beta-ensemble

Abstract: The characteristic polynomial of the Gaussian beta--ensemble can be represented, via its tridiagonal model, as an entry in a product of independent random two--by--two matrices. For a point z in the complex plane, at which the transfer matrix is to be evaluated, this product of transfer matrices splits into three independent factors, each of which can be understood as a different dynamical system in the complex plane. Conjecturally, we show that the characteristic polynomial is always represented as product of at most three terms, an exponential of a Gaussian field, the stochastic Airy function, and a diffusion similar to the stochastic sine equation. We explain the origins of this decomposition, and we show partial progress in establishing part of it.

Joint work with Diane Holcomb and Gaultier Lambert.

October 11, Chris Janjigian, University of Utah

Title: Busemann functions and Gibbs measures in directed polymer models on Z^2

Abstract: We consider the model of a nearest-neighbor random walk on the planar square lattice in a general iid space-time potential, which is also known as a directed polymer in a random environment. We prove results on existence, uniqueness (and non-uniqueness), and the law of large numbers for semi-infinite path measures. Our main tools are the Busemann functions, which are families of stochastic processes obtained through limits of ratios of partition functions.

Based on joint work with Firas Rassoul-Agha

October 18-20, Midwest Probability Colloquium, No Seminar

October 25, Promit Ghosal, Columbia

Title: Tails of the KPZ equation

Abstract: The KPZ equation is a fundamental stochastic PDE related to modeling random growth processes, Burgers turbulence, interacting particle system, random polymers etc. It is related to another important SPDE, namely, the stochastic heat equation (SHE). In this talk, we focus on the tail probabilities of the solution of the KPZ equation. For instance, we investigate the probability of the solution being smaller or larger than the expected value. Our analysis is based on an exact identity between the KPZ equation and the Airy point process (which arises at the edge of the spectrum of the random Hermitian matrices) and the Brownian Gibbs property of the KPZ line ensemble.

This talk will be based on a joint work with my advisor Prof. Ivan Corwin.

November 1, James Melbourne, University of Minnesota

Title: Upper bounds on the density of independent vectors under certain linear mappings

Abstract: Using functional analytic techniques and rearrangement, we prove anti-concentration results for the linear images of independent random variables, in the form of density upper bounds. For continuous variables the results unify and sharpen Bobkov-Chistyakov's for independent sums of vectors and Rudelson-Vershynin's bounds on projections of independent coordinates. For integer valued variables the techniques reduce finding the maximum of the probability mass function of a sum of independent variables, to the case that each variable is uniform on a contiguous interval. This problem is approached through analysis of characteristic functions and new $L^p$ bounds on the Dirichlet and Fejer Kernel are obtained and used to derive a discrete analog of Bobkov-Chistyakov.

November 8, Thomas Leblé, NYU

Title: The Sine-beta process: DLR equations and applications

Abstract: One-dimensional log-gases, or Beta-ensembles, are statistical physics models finding an incarnation in random matrix theory. Their limit behavior at microscopic scale is known as the Sine-beta process, its original description involves systems of coupled SDE's. In a joint work with D. Dereudre, A. Hardy, and M. Maïda, we give a new description of Sine-beta as an "infinite volume Gibbs measure", using the Dobrushin-Lanford-Ruelle (DLR) formalism, and we use it to prove the rigidity of the process, in the sense of Ghosh-Peres. Another application is a CLT for fluctuations of linear statistics.

November 22, Thanksgiving Break, No Seminar

Monday, November 26, 4pm, Van Vleck 911 Vadim Gorin, MIT

Please note the unusual day and time
and room.

Title: Macroscopic fluctuations through Schur generating functions

Abstract: I will talk about a special class of large-dimensional stochastic systems with strong correlations. The main examples will be random tilings, non-colliding random walks, eigenvalues of random matrices, and measures governing decompositions of group representations into irreducible components.

It is believed that macroscopic fluctuations in such systems are universally described by log-correlated Gaussian fields. I will present an approach to handle this question based on the notion of the Schur generating function of a probability distribution, and explain how it leads to a rigorous confirmation of this belief in a variety of situations.

Wednesday, December 5, Subhabrata Sen, MIT and Microsoft Research New England

Please note the unusual day and time

Past Seminars

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private $mTimestamp = NULL; private $mUser = class User { public $mId = 0; public $mName = '18.206.12.157'; public $mActorId = NULL; public $mRealName = ''; public $mEmail = ''; public $mTouched = '1'; protected $mQuickTouched = NULL; protected $mToken = NULL; public $mEmailAuthenticated = NULL; protected $mEmailToken = ''; protected $mEmailTokenExpires = NULL; protected $mRegistration = '20231129142952'; protected $mLoadedItems = TRUE; public $mFrom = 'session'; protected $mDatePreference = 'default'; private $mBlockedby = -1; protected $mHash = FALSE; protected $mBlockreason = NULL; protected $mGlobalBlock = NULL; protected $mLocked = NULL; private $mHideName = NULL; private $mRequest = class WebRequest { ... }; private $mBlock = NULL; private $mBlockedFromCreateAccount = FALSE; protected $queryFlagsUsed = 0; private $mThisAsAuthority = class MediaWiki\Permissions\UserAuthority { ... }; private $isTemp = NULL }; private $onAccessCallback = [0 => class ParserOutput { ... }, 1 => 'recordOption']; private $redirectTarget = NULL; private $mExtraKey = '' }, $revision = class MediaWiki\Revision\RevisionStoreRecord { protected $wikiId = FALSE; protected $mId = 16436; protected $mPageId = 92; protected $mUser = class MediaWiki\User\UserIdentityValue { private $id = 79; private $name = 'Pmwood'; private $wikiId = FALSE }; protected $mMinorEdit = FALSE; protected $mTimestamp = '20181121152130'; protected $mDeleted = 0; protected $mSize = 9476; protected $mSha1 = 'nka5h221ypgljoauw0ue9ae0cchukz4'; protected $mParentId = 16430; protected $mComment = class CommentStoreComment { public $id = '3202'; public $text = '/* Monday, November 26, 4pm Vadim Gorin, MIT */'; public $message = class RawMessage { ... }; public $data = NULL }; protected $mPage = class Title { private $mTextform = 'Past Probability Seminars Spring 2020'; private $mUrlform = 'Past_Probability_Seminars_Spring_2020'; private $mDbkeyform = 'Past_Probability_Seminars_Spring_2020'; private $mNamespace = 0; private $mInterwiki = ''; private $mLocalInterwiki = FALSE; private $mFragment = ''; public $mArticleID = 92; protected $mLatestID = FALSE; private $mContentModel = FALSE; private $mForcedContentModel = FALSE; private $mEstimateRevisions = NULL; public $prefixedText = NULL; protected $mLength = -1; public $mRedirect = NULL; private $mHasSubpages = NULL; private $mPageLanguage = NULL; private $mDbPageLanguage = FALSE; private $mTitleValue = NULL; private $mIsBigDeletion = NULL; private $mIsValid = NULL; private $mInstanceCacheKey = NULL; protected $deprecatedPublicProperties = [...]; private $dynamicPropertiesAccessDeprecated = FALSE }; protected $mSlots = class MediaWiki\Revision\RevisionSlots { protected $slots = [...] }; protected $mCurrent = FALSE }, $options = 5 )	.../Article.php:713
11	0.1207	2433648	PoolCounterWork->execute( $skipcache = ??? )	.../ParserOutputAccess.php:299
12	0.1207	2433840	PoolWorkArticleViewOld->doWork( )	.../PoolCounterWork.php:162
13	0.1208	2434096	PoolWorkArticleView->renderRevision( )	.../PoolWorkArticleViewOld.php:66
14	0.1209	2437120	MediaWiki\Revision\RenderedRevision->getRevisionParserOutput( $hints = ??? )	.../PoolWorkArticleView.php:91
15	0.1209	2437120	call_user_func:{/var/www/wiki_mediawiki-1.39.3/includes/Revision/RenderedRevision.php:199}( $callback = class Closure { public $this = class MediaWiki\Revision\RevisionRenderer { private $saveParseLogger = class MediaWiki\Logger\LegacyLogger { ... }; private $loadBalancer = class Wikimedia\Rdbms\LoadBalancer { ... }; private $roleRegistery = class MediaWiki\Revision\SlotRoleRegistry { ... }; private $contentRenderer = class MediaWiki\Content\Renderer\ContentRenderer { ... }; private $dbDomain = FALSE }; public $parameter = ['$rrev' => '<required>', '$hints' => '<required>'] }, $args = class MediaWiki\Revision\RenderedRevision { private $revision = class MediaWiki\Revision\RevisionStoreRecord { protected $wikiId = FALSE; protected $mId = 16436; protected $mPageId = 92; protected $mUser = class MediaWiki\User\UserIdentityValue { ... }; protected $mMinorEdit = FALSE; protected $mTimestamp = '20181121152130'; protected $mDeleted = 0; protected $mSize = 9476; protected $mSha1 = 'nka5h221ypgljoauw0ue9ae0cchukz4'; protected $mParentId = 16430; protected $mComment = class CommentStoreComment { ... }; protected $mPage = class Title { ... }; protected $mSlots = class MediaWiki\Revision\RevisionSlots { ... }; protected $mCurrent = FALSE }; private $options = class ParserOptions { private $options = [...]; private $mTimestamp = NULL; private $mUser = class User { ... }; private $onAccessCallback = [...]; private $redirectTarget = NULL; private $mExtraKey = '' }; private $audience = 3; private $performer = NULL; private $revisionOutput = NULL; private $slotsOutput = []; private $combineOutput = class Closure { public $this = class MediaWiki\Revision\RevisionRenderer { ... }; public $parameter = [...] }; private $saveParseLogger = class MediaWiki\Logger\LegacyLogger { protected $channel = 'SaveParse'; private $minimumLevel = 999; private $isDB = FALSE }; private $contentRenderer = class MediaWiki\Content\Renderer\ContentRenderer { private $contentHandlerFactory = class MediaWiki\Content\ContentHandlerFactory { ... } } }, [] )	.../RenderedRevision.php:199
16	0.1209	2437192	MediaWiki\Revision\RevisionRenderer->MediaWiki\Revision\{closure:/var/www/wiki_mediawiki-1.39.3/includes/Revision/RevisionRenderer.php:157-159}( $rrev = class MediaWiki\Revision\RenderedRevision { private $revision = class MediaWiki\Revision\RevisionStoreRecord { protected $wikiId = FALSE; protected $mId = 16436; protected $mPageId = 92; protected $mUser = class MediaWiki\User\UserIdentityValue { ... }; protected $mMinorEdit = FALSE; protected $mTimestamp = '20181121152130'; protected $mDeleted = 0; protected $mSize = 9476; protected $mSha1 = 'nka5h221ypgljoauw0ue9ae0cchukz4'; protected $mParentId = 16430; protected $mComment = class CommentStoreComment { ... }; protected $mPage = class Title { ... }; protected $mSlots = class MediaWiki\Revision\RevisionSlots { ... }; protected $mCurrent = FALSE }; private $options = class ParserOptions { private $options = [...]; private $mTimestamp = NULL; private $mUser = class User { ... }; private $onAccessCallback = [...]; private $redirectTarget = NULL; private $mExtraKey = '' }; private $audience = 3; private $performer = NULL; private $revisionOutput = NULL; private $slotsOutput = []; private $combineOutput = class Closure { public $this = class MediaWiki\Revision\RevisionRenderer { ... }; public $parameter = [...] }; private $saveParseLogger = class MediaWiki\Logger\LegacyLogger { protected $channel = 'SaveParse'; private $minimumLevel = 999; private $isDB = FALSE }; private $contentRenderer = class MediaWiki\Content\Renderer\ContentRenderer { private $contentHandlerFactory = class MediaWiki\Content\ContentHandlerFactory { ... } } }, $hints = [] )	.../RenderedRevision.php:199
17	0.1209	2437192	MediaWiki\Revision\RevisionRenderer->combineSlotOutput( $rrev = class MediaWiki\Revision\RenderedRevision { private $revision = class MediaWiki\Revision\RevisionStoreRecord { protected $wikiId = FALSE; protected $mId = 16436; protected $mPageId = 92; protected $mUser = class MediaWiki\User\UserIdentityValue { ... }; protected $mMinorEdit = FALSE; protected $mTimestamp = '20181121152130'; protected $mDeleted = 0; protected $mSize = 9476; protected $mSha1 = 'nka5h221ypgljoauw0ue9ae0cchukz4'; protected $mParentId = 16430; protected $mComment = class CommentStoreComment { ... }; protected $mPage = class Title { ... }; protected $mSlots = class MediaWiki\Revision\RevisionSlots { ... }; protected $mCurrent = FALSE }; private $options = class ParserOptions { private $options = [...]; private $mTimestamp = NULL; private $mUser = class User { ... }; private $onAccessCallback = [...]; private $redirectTarget = NULL; private $mExtraKey = '' }; private $audience = 3; private $performer = NULL; private $revisionOutput = NULL; private $slotsOutput = []; private $combineOutput = class Closure { public $this = class MediaWiki\Revision\RevisionRenderer { ... }; public $parameter = [...] }; private $saveParseLogger = class MediaWiki\Logger\LegacyLogger { protected $channel = 'SaveParse'; private $minimumLevel = 999; private $isDB = FALSE }; private $contentRenderer = class MediaWiki\Content\Renderer\ContentRenderer { private $contentHandlerFactory = class MediaWiki\Content\ContentHandlerFactory { ... } } }, $hints = [] )	.../RevisionRenderer.php:158
18	0.1219	2438768	MediaWiki\Revision\RenderedRevision->getSlotParserOutput( $role = 'main', $hints = [] )	.../RevisionRenderer.php:221
19	0.1233	2452560	MediaWiki\Revision\RenderedRevision->getSlotParserOutputUncached( $content = class WikitextContent { protected $model_id = 'wikitext'; protected $mText = '__NOTOC__\n\n= Fall 2018 =\n\n<b>Thursdays in 901 Van Vleck Hall at 2:25 PM</b>, unless otherwise noted. \n<b>We usually end for questions at 3:15 PM.</b>\n\nIf you would like to sign up for the email list to receive seminar announcements then please send an email to \n[mailto:join-probsem@lists.wisc.edu join-probsem@lists.wisc.edu]\n\n\n\n==<span style="color:red"> Friday, August 10, 10am, B239 Van Vleck </span> András Mészáros, Central European University, Budapest ==\n\n\nTitle: \'\'\'The distribution of sandpile grou'...; private $redirectTargetAndText = [0 => NULL, 1 => '__NOTOC__\n\n= Fall 2018 =\n\n<b>Thursdays in 901 Van Vleck Hall at 2:25 PM</b>, unless otherwise noted. \n<b>We usually end for questions at 3:15 PM.</b>\n\nIf you would like to sign up for the email list to receive seminar announcements then please send an email to \n[mailto:join-probsem@lists.wisc.edu join-probsem@lists.wisc.edu]\n\n\n\n==<span style="color:red"> Friday, August 10, 10am, B239 Van Vleck </span> András Mészáros, Central European University, Budapest ==\n\n\nTitle: \'\'\'The distribution of sandpile grou'...]; private $preSaveTransformFlags = [] }, $withHtml = TRUE )	.../RenderedRevision.php:237
20	0.1233	2452560	MediaWiki\Content\Renderer\ContentRenderer->getParserOutput( $content = class WikitextContent { protected $model_id = 'wikitext'; protected $mText = '__NOTOC__\n\n= Fall 2018 =\n\n<b>Thursdays in 901 Van Vleck Hall at 2:25 PM</b>, unless otherwise noted. \n<b>We usually end for questions at 3:15 PM.</b>\n\nIf you would like to sign up for the email list to receive seminar announcements then please send an email to \n[mailto:join-probsem@lists.wisc.edu join-probsem@lists.wisc.edu]\n\n\n\n==<span style="color:red"> Friday, August 10, 10am, B239 Van Vleck </span> András Mészáros, Central European University, Budapest ==\n\n\nTitle: \'\'\'The distribution of sandpile grou'...; private $redirectTargetAndText = [0 => NULL, 1 => '__NOTOC__\n\n= Fall 2018 =\n\n<b>Thursdays in 901 Van Vleck Hall at 2:25 PM</b>, unless otherwise noted. \n<b>We usually end for questions at 3:15 PM.</b>\n\nIf you would like to sign up for the email list to receive seminar announcements then please send an email to \n[mailto:join-probsem@lists.wisc.edu join-probsem@lists.wisc.edu]\n\n\n\n==<span style="color:red"> Friday, August 10, 10am, B239 Van Vleck </span> András Mészáros, Central European University, Budapest ==\n\n\nTitle: \'\'\'The distribution of sandpile grou'...]; private $preSaveTransformFlags = [] }, $page = class Title { private $mTextform = 'Past Probability Seminars Spring 2020'; private $mUrlform = 'Past_Probability_Seminars_Spring_2020'; private $mDbkeyform = 'Past_Probability_Seminars_Spring_2020'; private $mNamespace = 0; private $mInterwiki = ''; private $mLocalInterwiki = FALSE; private $mFragment = ''; public $mArticleID = 92; protected $mLatestID = FALSE; private $mContentModel = FALSE; private $mForcedContentModel = FALSE; private $mEstimateRevisions = NULL; public $prefixedText = NULL; protected $mLength = -1; public $mRedirect = NULL; private $mHasSubpages = NULL; private $mPageLanguage = NULL; private $mDbPageLanguage = FALSE; private $mTitleValue = NULL; private $mIsBigDeletion = NULL; private $mIsValid = NULL; private $mInstanceCacheKey = NULL; protected $deprecatedPublicProperties = ['mTextform' => [...], 'mUrlform' => [...], 'mDbkeyform' => [...], 'mNamespace' => [...], 'mInterwiki' => [...], 'mFragment' => [...]]; private $dynamicPropertiesAccessDeprecated = FALSE }, $revId = 16436, $parserOptions = class ParserOptions { private $options = ['dateformat' => 'default', 'speculativeRevId' => NULL, 'speculativePageId' => NULL, 'interfaceMessage' => FALSE, 'targetLanguage' => NULL, 'removeComments' => TRUE, 'suppressTOC' => FALSE, 'enableLimitReport' => FALSE, 'preSaveTransform' => TRUE, 'isPreview' => FALSE, 'isSectionPreview' => FALSE, 'printable' => FALSE, 'allowUnsafeRawHtml' => TRUE, 'wrapclass' => 'mw-parser-output', 'currentRevisionRecordCallback' => class Closure { ... }, 'templateCallback' => [...], 'speculativeRevIdCallback' => class Closure { ... }, 'speculativePageIdCallback' => class Closure { ... }, 'interwikiMagic' => TRUE, 'allowExternalImages' => FALSE, 'allowExternalImagesFrom' => '', 'enableImageWhitelist' => FALSE, 'allowSpecialInclusion' => TRUE, 'maxIncludeSize' => 2097152, 'maxPPNodeCount' => 1000000, 'maxPPExpandDepth' => 100, 'maxTemplateDepth' => 100, 'expensiveParserFunctionLimit' => 100, 'externalLinkTarget' => FALSE, 'cleanSignatures' => TRUE, 'disableContentConversion' => FALSE, 'disableTitleConversion' => FALSE, 'magicISBNLinks' => FALSE, 'magicPMIDLinks' => FALSE, 'magicRFCLinks' => FALSE, 'thumbsize' => 5, 'userlang' => class LanguageEn { ... }]; private $mTimestamp = NULL; private $mUser = class User { public $mId = 0; public $mName = '18.206.12.157'; public $mActorId = NULL; public $mRealName = ''; public $mEmail = ''; public $mTouched = '1'; protected $mQuickTouched = NULL; protected $mToken = NULL; public $mEmailAuthenticated = NULL; protected $mEmailToken = ''; protected $mEmailTokenExpires = NULL; protected $mRegistration = '20231129142952'; protected $mLoadedItems = TRUE; public $mFrom = 'session'; protected $mDatePreference = 'default'; private $mBlockedby = -1; protected $mHash = FALSE; protected $mBlockreason = NULL; protected $mGlobalBlock = NULL; protected $mLocked = NULL; private $mHideName = NULL; private $mRequest = class WebRequest { ... }; private $mBlock = NULL; private $mBlockedFromCreateAccount = FALSE; protected $queryFlagsUsed = 0; private $mThisAsAuthority = class MediaWiki\Permissions\UserAuthority { ... }; private $isTemp = NULL }; private $onAccessCallback = [0 => class ParserOutput { ... }, 1 => 'recordOption']; private $redirectTarget = NULL; private $mExtraKey = '' }, $generateHtml = TRUE )	.../RenderedRevision.php:265
21	0.1233	2452672	ContentHandler->getParserOutput( $content = class WikitextContent { protected $model_id = 'wikitext'; protected $mText = '__NOTOC__\n\n= Fall 2018 =\n\n<b>Thursdays in 901 Van Vleck Hall at 2:25 PM</b>, unless otherwise noted. \n<b>We usually end for questions at 3:15 PM.</b>\n\nIf you would like to sign up for the email list to receive seminar announcements then please send an email to \n[mailto:join-probsem@lists.wisc.edu join-probsem@lists.wisc.edu]\n\n\n\n==<span style="color:red"> Friday, August 10, 10am, B239 Van Vleck </span> András Mészáros, Central European University, Budapest ==\n\n\nTitle: \'\'\'The distribution of sandpile grou'...; private $redirectTargetAndText = [0 => NULL, 1 => '__NOTOC__\n\n= Fall 2018 =\n\n<b>Thursdays in 901 Van Vleck Hall at 2:25 PM</b>, unless otherwise noted. \n<b>We usually end for questions at 3:15 PM.</b>\n\nIf you would like to sign up for the email list to receive seminar announcements then please send an email to \n[mailto:join-probsem@lists.wisc.edu join-probsem@lists.wisc.edu]\n\n\n\n==<span style="color:red"> Friday, August 10, 10am, B239 Van Vleck </span> András Mészáros, Central European University, Budapest ==\n\n\nTitle: \'\'\'The distribution of sandpile grou'...]; private $preSaveTransformFlags = [] }, $cpoParams = class MediaWiki\Content\Renderer\ContentParseParams { private $page = class Title { private $mTextform = 'Past Probability Seminars Spring 2020'; private $mUrlform = 'Past_Probability_Seminars_Spring_2020'; private $mDbkeyform = 'Past_Probability_Seminars_Spring_2020'; private $mNamespace = 0; private $mInterwiki = ''; private $mLocalInterwiki = FALSE; private $mFragment = ''; public $mArticleID = 92; protected $mLatestID = FALSE; private $mContentModel = FALSE; private $mForcedContentModel = FALSE; private $mEstimateRevisions = NULL; public $prefixedText = NULL; protected $mLength = -1; public $mRedirect = NULL; private $mHasSubpages = NULL; private $mPageLanguage = NULL; private $mDbPageLanguage = FALSE; private $mTitleValue = NULL; private $mIsBigDeletion = NULL; private $mIsValid = NULL; private $mInstanceCacheKey = NULL; protected $deprecatedPublicProperties = [...]; private $dynamicPropertiesAccessDeprecated = FALSE }; private $revId = 16436; private $parserOptions = class ParserOptions { private $options = [...]; private $mTimestamp = NULL; private $mUser = class User { ... }; private $onAccessCallback = [...]; private $redirectTarget = NULL; private $mExtraKey = '' }; private $generateHtml = TRUE } )	.../ContentRenderer.php:47
22	0.1235	2454768	WikitextContentHandler->fillParserOutput( $content = class WikitextContent { protected $model_id = 'wikitext'; protected $mText = '__NOTOC__\n\n= Fall 2018 =\n\n<b>Thursdays in 901 Van Vleck Hall at 2:25 PM</b>, unless otherwise noted. \n<b>We usually end for questions at 3:15 PM.</b>\n\nIf you would like to sign up for the email list to receive seminar announcements then please send an email to \n[mailto:join-probsem@lists.wisc.edu join-probsem@lists.wisc.edu]\n\n\n\n==<span style="color:red"> Friday, August 10, 10am, B239 Van Vleck </span> András Mészáros, Central European University, Budapest ==\n\n\nTitle: \'\'\'The distribution of sandpile grou'...; private $redirectTargetAndText = [0 => NULL, 1 => '__NOTOC__\n\n= Fall 2018 =\n\n<b>Thursdays in 901 Van Vleck Hall at 2:25 PM</b>, unless otherwise noted. \n<b>We usually end for questions at 3:15 PM.</b>\n\nIf you would like to sign up for the email list to receive seminar announcements then please send an email to \n[mailto:join-probsem@lists.wisc.edu join-probsem@lists.wisc.edu]\n\n\n\n==<span style="color:red"> Friday, August 10, 10am, B239 Van Vleck </span> András Mészáros, Central European University, Budapest ==\n\n\nTitle: \'\'\'The distribution of sandpile grou'...]; private $preSaveTransformFlags = [] }, $cpoParams = class MediaWiki\Content\Renderer\ContentParseParams { private $page = class Title { private $mTextform = 'Past Probability Seminars Spring 2020'; private $mUrlform = 'Past_Probability_Seminars_Spring_2020'; private $mDbkeyform = 'Past_Probability_Seminars_Spring_2020'; private $mNamespace = 0; private $mInterwiki = ''; private $mLocalInterwiki = FALSE; private $mFragment = ''; public $mArticleID = 92; protected $mLatestID = FALSE; private $mContentModel = FALSE; private $mForcedContentModel = FALSE; private $mEstimateRevisions = NULL; public $prefixedText = NULL; protected $mLength = -1; public $mRedirect = NULL; private $mHasSubpages = NULL; private $mPageLanguage = NULL; private $mDbPageLanguage = FALSE; private $mTitleValue = NULL; private $mIsBigDeletion = NULL; private $mIsValid = NULL; private $mInstanceCacheKey = NULL; protected $deprecatedPublicProperties = [...]; private $dynamicPropertiesAccessDeprecated = FALSE }; private $revId = 16436; private $parserOptions = class ParserOptions { private $options = [...]; private $mTimestamp = NULL; private $mUser = class User { ... }; private $onAccessCallback = [...]; private $redirectTarget = NULL; private $mExtraKey = '' }; private $generateHtml = TRUE }, $parserOutput = class ParserOutput { protected $mParseUsedOptions = []; protected $mCacheTime = ''; protected $mCacheExpiry = NULL; protected $mCacheRevisionId = NULL; private $mText = NULL; private $mLanguageLinks = []; private $mCategories = []; private $mIndicators = []; private $mTitleText = ''; private $mLinks = []; private $mLinksSpecial = []; private $mTemplates = []; private $mTemplateIds = []; private $mImages = []; private $mFileSearchOptions = []; private $mExternalLinks = []; private $mInterwikiLinks = []; private $mNewSection = FALSE; private $mHideNewSection = FALSE; private $mNoGallery = FALSE; private $mHeadItems = []; private $mModules = []; private $mModuleStyles = []; private $mJsConfigVars = []; private $mOutputHooks = []; private $mWarnings = []; private $mWarningMsgs = []; private $mSections = []; private $mProperties = []; private $mTOCHTML = ''; private $mTimestamp = NULL; private $mEnableOOUI = FALSE; private $mIndexSet = FALSE; private $mNoIndexSet = FALSE; private $mExtensionData = []; private $mLimitReportData = []; private $mLimitReportJSData = []; private $mCacheMessage = ''; private $mParseStartTime = []; private $mPreventClickjacking = FALSE; private $mExtraScriptSrcs = []; private $mExtraDefaultSrcs = []; private $mExtraStyleSrcs = []; private $mFlags = []; private $mSpeculativeRevId = NULL; private $speculativePageIdUsed = NULL; private $revisionTimestampUsed = NULL; private $revisionUsedSha1Base36 = NULL; private $mWrapperDivClasses = []; private $mMaxAdaptiveExpiry = INF } )	.../ContentHandler.php:1720
23	0.1235	2454768	Parser->parse( $text = '__NOTOC__\n\n= Fall 2018 =\n\n<b>Thursdays in 901 Van Vleck Hall at 2:25 PM</b>, unless otherwise noted. \n<b>We usually end for questions at 3:15 PM.</b>\n\nIf you would like to sign up for the email list to receive seminar announcements then please send an email to \n[mailto:join-probsem@lists.wisc.edu join-probsem@lists.wisc.edu]\n\n\n\n==<span style="color:red"> Friday, August 10, 10am, B239 Van Vleck </span> András Mészáros, Central European University, Budapest ==\n\n\nTitle: \'\'\'The distribution of sandpile grou'..., $page = class Title { private $mTextform = 'Past Probability Seminars Spring 2020'; private $mUrlform = 'Past_Probability_Seminars_Spring_2020'; private $mDbkeyform = 'Past_Probability_Seminars_Spring_2020'; private $mNamespace = 0; private $mInterwiki = ''; private $mLocalInterwiki = FALSE; private $mFragment = ''; public $mArticleID = 92; protected $mLatestID = FALSE; private $mContentModel = FALSE; private $mForcedContentModel = FALSE; private $mEstimateRevisions = NULL; public $prefixedText = NULL; protected $mLength = -1; public $mRedirect = NULL; private $mHasSubpages = NULL; private $mPageLanguage = NULL; private $mDbPageLanguage = FALSE; private $mTitleValue = NULL; private $mIsBigDeletion = NULL; private $mIsValid = NULL; private $mInstanceCacheKey = NULL; protected $deprecatedPublicProperties = ['mTextform' => [...], 'mUrlform' => [...], 'mDbkeyform' => [...], 'mNamespace' => [...], 'mInterwiki' => [...], 'mFragment' => [...]]; private $dynamicPropertiesAccessDeprecated = FALSE }, $options = class ParserOptions { private $options = ['dateformat' => 'default', 'speculativeRevId' => NULL, 'speculativePageId' => NULL, 'interfaceMessage' => FALSE, 'targetLanguage' => NULL, 'removeComments' => TRUE, 'suppressTOC' => FALSE, 'enableLimitReport' => FALSE, 'preSaveTransform' => TRUE, 'isPreview' => FALSE, 'isSectionPreview' => FALSE, 'printable' => FALSE, 'allowUnsafeRawHtml' => TRUE, 'wrapclass' => 'mw-parser-output', 'currentRevisionRecordCallback' => class Closure { ... }, 'templateCallback' => [...], 'speculativeRevIdCallback' => class Closure { ... }, 'speculativePageIdCallback' => class Closure { ... }, 'interwikiMagic' => TRUE, 'allowExternalImages' => FALSE, 'allowExternalImagesFrom' => '', 'enableImageWhitelist' => FALSE, 'allowSpecialInclusion' => TRUE, 'maxIncludeSize' => 2097152, 'maxPPNodeCount' => 1000000, 'maxPPExpandDepth' => 100, 'maxTemplateDepth' => 100, 'expensiveParserFunctionLimit' => 100, 'externalLinkTarget' => FALSE, 'cleanSignatures' => TRUE, 'disableContentConversion' => FALSE, 'disableTitleConversion' => FALSE, 'magicISBNLinks' => FALSE, 'magicPMIDLinks' => FALSE, 'magicRFCLinks' => FALSE, 'thumbsize' => 5, 'userlang' => class LanguageEn { ... }]; private $mTimestamp = NULL; private $mUser = class User { public $mId = 0; public $mName = '18.206.12.157'; public $mActorId = NULL; public $mRealName = ''; public $mEmail = ''; public $mTouched = '1'; protected $mQuickTouched = NULL; protected $mToken = NULL; public $mEmailAuthenticated = NULL; protected $mEmailToken = ''; protected $mEmailTokenExpires = NULL; protected $mRegistration = '20231129142952'; protected $mLoadedItems = TRUE; public $mFrom = 'session'; protected $mDatePreference = 'default'; private $mBlockedby = -1; protected $mHash = FALSE; protected $mBlockreason = NULL; protected $mGlobalBlock = NULL; protected $mLocked = NULL; private $mHideName = NULL; private $mRequest = class WebRequest { ... }; private $mBlock = NULL; private $mBlockedFromCreateAccount = FALSE; protected $queryFlagsUsed = 0; private $mThisAsAuthority = class MediaWiki\Permissions\UserAuthority { ... }; private $isTemp = NULL }; private $onAccessCallback = [0 => class ParserOutput { ... }, 1 => 'recordOption']; private $redirectTarget = NULL; private $mExtraKey = '' }, $linestart = TRUE, $clearState = TRUE, $revid = 16436 )	.../WikitextContentHandler.php:301
24	0.1236	2462040	Parser->internalParse( $text = '__NOTOC__\n\n= Fall 2018 =\n\n<b>Thursdays in 901 Van Vleck Hall at 2:25 PM</b>, unless otherwise noted. \n<b>We usually end for questions at 3:15 PM.</b>\n\nIf you would like to sign up for the email list to receive seminar announcements then please send an email to \n[mailto:join-probsem@lists.wisc.edu join-probsem@lists.wisc.edu]\n\n\n\n==<span style="color:red"> Friday, August 10, 10am, B239 Van Vleck </span> András Mészáros, Central European University, Budapest ==\n\n\nTitle: \'\'\'The distribution of sandpile grou'..., $isMain = ???, $frame = ??? )	.../Parser.php:724
25	0.1236	2462072	Parser->replaceVariables( $text = '__NOTOC__\n\n= Fall 2018 =\n\n<b>Thursdays in 901 Van Vleck Hall at 2:25 PM</b>, unless otherwise noted. \n<b>We usually end for questions at 3:15 PM.</b>\n\nIf you would like to sign up for the email list to receive seminar announcements then please send an email to \n[mailto:join-probsem@lists.wisc.edu join-probsem@lists.wisc.edu]\n\n\n\n==<span style="color:red"> Friday, August 10, 10am, B239 Van Vleck </span> András Mészáros, Central European University, Budapest ==\n\n\nTitle: \'\'\'The distribution of sandpile grou'..., $frame = ???, $argsOnly = ??? )	.../Parser.php:1610
26	0.1256	2512760	PPFrame_Hash->expand( $root = class PPNode_Hash_Tree { public $name = 'root'; private $rawChildren = [0 => '__NOTOC__\n\n', 1 => [...], 2 => '\n\n<b>Thursdays in 901 Van Vleck Hall at 2:25 PM</b>, unless otherwise noted. \n<b>We usually end for questions at 3:15 PM.</b>\n\nIf you would like to sign up for the email list to receive seminar announcements then please send an email to \n[mailto:join-probsem@lists.wisc.edu join-probsem@lists.wisc.edu]\n\n\n\n', 3 => [...], 4 => '\n\n\nTitle: \'\'\'The distribution of sandpile groups of random regular graphs\'\'\'\n\nAbstract:\nWe study the distribution of the sandpile group of random ', 5 => [...], 6 => '-regular graphs. For the directed model we prove that it follows the Cohen-Lenstra heuristics, that is, the probability that the ', 7 => [...], 8 => '-Sylow subgroup of the sandpile group is a given ', 9 => [...], 10 => '-group ', 11 => [...], 12 => ', is proportional to ', 13 => [...], 14 => '. For finitely many primes, these events get independent in limit. Similar results hold for undirected random regular graphs, there for odd primes the limiting distributions are the ones given by Clancy, Leake and Payne.\n\nOur results extends a recent theorem of Huang saying that the adjacency matrices of random ', 15 => [...], 16 => '-regular directed graphs are invertible with high probability to the undirected case.\n\n', 17 => [...], 18 => '\n', 19 => [...], 20 => '\n\nTitle: \'\'\'Stochastic quantization of Yang-Mills\'\'\'\n\nAbstract:\n"Stochastic quantization” refers to a formulation of quantum field theory as stochastic PDEs. Interesting progress has been made these years in understanding these SPDEs, examples including Phi4 and sine-Gordon. Yang-Mills is a type of quantum field theory which has gauge symmetry, and its stochastic quantization is a Yang-Mills flow perturbed by white noise.\nIn this talk we start by an Abelian example where we take a symmetry-preserving latt'..., 21 => [...], 22 => '\n\nTitle:\'\'\'Random walk in random environment and the Kardar-Parisi-Zhang class\'\'\'\n \nAbstract:This talk concerns a relationship between two much-studied classes of models of motion in a random medium, namely random walk in random environment (RWRE) and the Kardar-Parisi-Zhang (KPZ) universality class. Barraquand and Corwin (Columbia) discovered that in 1+1 dimensional RWRE in a dynamical beta environment the correction to the quenched large deviation principle obeys KPZ behavior. In this talk we condition'..., 23 => [...], 24 => '\n\nTitle: \'\'\'Distributional approximation of the characteristic polynomial of a Gaussian beta-ensemble\'\'\'\n\nAbstract:\nThe characteristic polynomial of the Gaussian beta--ensemble can be represented, via its tridiagonal model, as an entry in a product of independent random two--by--two matrices. For a point z in the complex plane, at which the transfer matrix is to be evaluated, this product of transfer matrices splits into three independent factors, each of which can be understood as a different dynamical sy'..., 25 => [...], 26 => '\n\n\nTitle: \'\'\'Busemann functions and Gibbs measures in directed polymer models on Z^2\'\'\'\n\nAbstract: We consider the model of a nearest-neighbor random walk on the planar square lattice in a general iid space-time potential, which is also known as a directed polymer in a random environment. We prove results on existence, uniqueness (and non-uniqueness), and the law of large numbers for semi-infinite path measures. Our main tools are the Busemann functions, which are families of stochastic processes obtained t'..., 27 => [...], 28 => '\n\n', 29 => [...], 30 => '\n\n\nTitle: \'\'\'Tails of the KPZ equation\'\'\'\n \nAbstract: The KPZ equation is a fundamental stochastic PDE related to modeling random growth processes, Burgers turbulence, interacting particle system, random polymers etc. It is related to another important SPDE, namely, the stochastic heat equation (SHE). In this talk, we focus on the tail probabilities of the solution of the KPZ equation. For instance, we investigate the probability of the solution being smaller or larger than the expected value. Our anal'..., 31 => [...], 32 => '\n\nTitle: \'\'\'Upper bounds on the density of independent vectors under certain linear mappings\'\'\'\n\nAbstract: Using functional analytic techniques and rearrangement, we prove anti-concentration results for the linear images of independent random variables, in the form of density upper bounds. For continuous variables the results unify and sharpen Bobkov-Chistyakov\'s for independent sums of vectors and Rudelson-Vershynin\'s bounds on projections of independent coordinates. For integer valued variables the tec'..., 33 => [...], 34 => '\n\nTitle: \'\'\'The Sine-beta process: DLR equations and applications\'\'\'\n\nAbstract:\nOne-dimensional log-gases, or Beta-ensembles, are statistical physics models finding an incarnation in random matrix theory. Their limit behavior at microscopic scale is known as the Sine-beta process, its original description involves systems of coupled SDE\'s. In a joint work with D. Dereudre, A. Hardy, and M. Maïda, we give a new description of Sine-beta as an "infinite volume Gibbs measure", using the Dobrushin-Lanford-Ruell'..., 35 => [...], 36 => '\n', 37 => [...], 38 => '\n\n', 39 => [...], 40 => '\n\n\n<div style="width:320px;height:50px;border:5px solid black">\n<b><span style="color:red"> Please note the unusual day and time <br>\nand room.</span></b>\n</div>\n\nTitle: \'\'\'Macroscopic fluctuations through Schur generating functions\'\'\'\n\nAbstract:\nI will talk about a special class of large-dimensional stochastic systems with\nstrong correlations. The main examples will be random tilings, non-colliding random walks, eigenvalues of random matrices,\nand measures governing decompositions of group representations '..., 41 => [...], 42 => '\n', 43 => [...], 44 => '\n\n\n<div style="width:320px;height:50px;border:5px solid black">\n<b><span style="color:red"> Please note the unusual day and time </span></b>\n</div>\n\n', 45 => [...], 46 => '\n', 47 => [...], 48 => '\n\n', 49 => '[[Past Seminars]]']; private $store = [0 => [...]]; private $index = 0 }, $flags = 0 )	.../Parser.php:2955
27	0.1257	2516896	Parser->extensionSubstitution( $params = ['name' => class PPNode_Hash_Tree { public $name = 'name'; private $rawChildren = [...]; private $store = [...]; private $index = 0 }, 'attr' => class PPNode_Hash_Tree { public $name = 'attr'; private $rawChildren = [...]; private $store = [...]; private $index = 1 }, 'inner' => class PPNode_Hash_Tree { public $name = 'inner'; private $rawChildren = [...]; private $store = [...]; private $index = 2 }, 'close' => class PPNode_Hash_Tree { public $name = 'close'; private $rawChildren = [...]; private $store = [...]; private $index = 3 }], $frame = class PPFrame_Hash { public $parser = class Parser { private $mTagHooks = [...]; private $mFunctionHooks = [...]; private $mFunctionSynonyms = [...]; private $mStripList = [...]; private $mVarCache = [...]; private $mImageParams = [...]; private $mImageParamsMagicArray = [...]; public $mMarkerIndex = 1; private $mVariables = class MagicWordArray { ... }; private $mSubstWords = class MagicWordArray { ... }; private $mExtLinkBracketedRegex = '/\\[(((?i)bitcoin\\:\|ftp\\:\\/\\/\|ftps\\:\\/\\/\|geo\\:\|git\\:\\/\\/\|gopher\\:\\/\\/\|http\\:\\/\\/\|https\\:\\/\\/\|irc\\:\\/\\/\|ircs\\:\\/\\/\|magnet\\:\|mailto\\:\|matrix\\:\|mms\\:\\/\\/\|news\\:\|nntp\\:\\/\\/\|redis\\:\\/\\/\|sftp\\:\\/\\/\|sip\\:\|sips\\:\|sms\\:\|ssh\\:\\/\\/\|svn\\:\\/\\/\|tel\\:\|telnet\\:\\/\\/\|urn\\:\|worldwind\\:\\/\\/\|xmpp\\:\|\\/\\/)(?:[0-9.]+\|\\[(?i:[0-9a-f:.]+)\\]\|[^][<>"\\x00-\\x20\\x7F\\p{Zs}\\x{FFFD}])[^][<>"\\x00-\\x20\\x7F\\p{Zs}\\x{FFFD}])\\p{Zs}([^\\]\\x00-\\x08\\x0a-\\x1F\\x{FFFD}]*?)\\]/Su'; private $urlUtils = class MediaWiki\Utils\UrlUtils { ... }; private $mPreprocessor = class Preprocessor_Hash { ... }; private $mOutput = class ParserOutput { ... }; private $mAutonumber = 0; private $mStripState = class StripState { ... }; private $mLinkHolders = class LinkHolderArray { ... }; private $mLinkID = 0; private $mIncludeSizes = [...]; public $mPPNodeCount = 6; public $mHighestExpansionDepth = 2; private $mTplRedirCache = [...]; public $mHeadings = [...]; private $mDoubleUnderscores = [...]; public $mExpensiveFunctionCount = 0; private $mShowToc = TRUE; private $mForceTocPosition = FALSE; private $mTplDomCache = [...]; private $mUser = NULL; public $mOptions = class ParserOptions { ... }; public $mTitle = class Title { ... }; private $mOutputType = 1; public $ot = [...]; private $mRevisionId = 16436; private $mRevisionTimestamp = NULL; private $mRevisionUser = NULL; private $mRevisionSize = NULL; private $mInputSize = 9476; private $mRevisionRecordObject = NULL; private $mLangLinkLanguages = [...]; private $currentRevisionCache = NULL; private $mInParse = '#0 /var/www/wiki_mediawiki-1.39.3/includes/parser/Parser.php(699): Parser->lock()\n#1 /var/www/wiki_mediawiki-1.39.3/includes/content/WikitextContentHandler.php(301): Parser->parse()\n#2 /var/www/wiki_mediawiki-1.39.3/includes/content/ContentHandler.php(1720): WikitextContentHandler->fillParserOutput()\n#3 /var/www/wiki_mediawiki-1.39.3/includes/content/Renderer/ContentRenderer.php(47): ContentHandler->getParserOutput()\n#4 /var/www/wiki_mediawiki-1.39.3/includes/Revision/RenderedRevision.php(265): MediaWiki\\Co'...; private $mProfiler = class SectionProfiler { ... }; private $mLinkRenderer = NULL; private $magicWordFactory = class MagicWordFactory { ... }; private $contLang = class LanguageEn { ... }; private $languageConverterFactory = class MediaWiki\Languages\LanguageConverterFactory { ... }; private $factory = class ParserFactory { ... }; private $specialPageFactory = class MediaWiki\SpecialPage\SpecialPageFactory { ... }; private $titleFormatter = class MediaWikiTitleCodec { ... }; private $svcOptions = class MediaWiki\Config\ServiceOptions { ... }; private $linkRendererFactory = class MediaWiki\Linker\LinkRendererFactory { ... }; private $nsInfo = class NamespaceInfo { ... }; private $logger = class MediaWiki\Logger\LegacyLogger { ... }; private $badFileLookup = class MediaWiki\BadFileLookup { ... }; private $hookContainer = class MediaWiki\HookContainer\HookContainer { ... }; private $hookRunner = class MediaWiki\HookContainer\HookRunner { ... }; private $tidy = class MediaWiki\Tidy\RemexDriver { ... }; private $userOptionsLookup = class MediaWiki\User\UserOptionsManager { ... }; private $userFactory = class MediaWiki\User\UserFactory { ... }; private $httpRequestFactory = class MediaWiki\Http\HttpRequestFactory { ... }; private $trackingCategories = class TrackingCategories { ... }; private $signatureValidatorFactory = class MediaWiki\Preferences\SignatureValidatorFactory { ... }; private $userNameUtils = class MediaWiki\User\UserNameUtils { ... }; protected $deprecatedPublicProperties = [...]; private $dynamicPropertiesAccessDeprecated = FALSE }; public $preprocessor = class Preprocessor_Hash { public $parser = class Parser { ... }; protected $wanCache = class WANObjectCache { ... }; protected $disableLangConversion = FALSE; protected $rules = [...]; protected $cacheThreshold = 1000 }; public $title = class Title { private $mTextform = 'Past Probability Seminars Spring 2020'; private $mUrlform = 'Past_Probability_Seminars_Spring_2020'; private $mDbkeyform = 'Past_Probability_Seminars_Spring_2020'; private $mNamespace = 0; private $mInterwiki = ''; private $mLocalInterwiki = FALSE; private $mFragment = ''; public $mArticleID = 92; protected $mLatestID = FALSE; private $mContentModel = FALSE; private $mForcedContentModel = FALSE; private $mEstimateRevisions = NULL; public $prefixedText = NULL; protected $mLength = -1; public $mRedirect = NULL; private $mHasSubpages = NULL; private $mPageLanguage = NULL; private $mDbPageLanguage = FALSE; private $mTitleValue = NULL; private $mIsBigDeletion = NULL; private $mIsValid = NULL; private $mInstanceCacheKey = NULL; protected $deprecatedPublicProperties = [...]; private $dynamicPropertiesAccessDeprecated = FALSE }; public $titleCache = [0 => 'Past_Probability_Seminars_Spring_2020']; public $loopCheckHash = []; public $depth = 0; private $volatile = FALSE; private $ttl = NULL; protected $childExpansionCache = []; private $maxPPNodeCount = 1000000; private $maxPPExpandDepth = 100 }, $processNowiki = FALSE )	.../PPFrame_Hash.php:353
28	0.1258	2517400	SimpleMathJaxHooks::renderMath( $tex = 'd', $args = [], $parser = class Parser { private $mTagHooks = ['pre' => [...], 'nowiki' => [...], 'gallery' => [...], 'indicator' => [...], 'langconvert' => [...], 'math' => 'SimpleMathJaxHooks::renderMath', 'chem' => 'SimpleMathJaxHooks::renderChem', 'source' => [...], 'syntaxhighlight' => [...], 'ref' => [...], 'references' => [...]]; private $mFunctionHooks = ['ns' => [...], 'nse' => [...], 'urlencode' => [...], 'lcfirst' => [...], 'ucfirst' => [...], 'lc' => [...], 'uc' => [...], 'localurl' => [...], 'localurle' => [...], 'fullurl' => [...], 'fullurle' => [...], 'canonicalurl' => [...], 'canonicalurle' => [...], 'formatnum' => [...], 'grammar' => [...], 'gender' => [...], 'plural' => [...], 'bidi' => [...], 'numberofpages' => [...], 'numberofusers' => [...], 'numberofactiveusers' => [...], 'numberofarticles' => [...], 'numberoffiles' => [...], 'numberofadmins' => [...], 'numberingroup' => [...], 'numberofedits' => [...], 'language' => [...], 'padleft' => [...], 'padright' => [...], 'anchorencode' => [...], 'defaultsort' => [...], 'filepath' => [...], 'pagesincategory' => [...], 'pagesize' => [...], 'protectionlevel' => [...], 'protectionexpiry' => [...], 'namespace' => [...], 'namespacee' => [...], 'namespacenumber' => [...], 'talkspace' => [...], 'talkspacee' => [...], 'subjectspace' => [...], 'subjectspacee' => [...], 'pagename' => [...], 'pagenamee' => [...], 'fullpagename' => [...], 'fullpagenamee' => [...], 'rootpagename' => [...], 'rootpagenamee' => [...], 'basepagename' => [...], 'basepagenamee' => [...], 'subpagename' => [...], 'subpagenamee' => [...], 'talkpagename' => [...], 'talkpagenamee' => [...], 'subjectpagename' => [...], 'subjectpagenamee' => [...], 'pageid' => [...], 'revisionid' => [...], 'revisionday' => [...], 'revisionday2' => [...], 'revisionmonth' => [...], 'revisionmonth1' => [...], 'revisionyear' => [...], 'revisiontimestamp' => [...], 'revisionuser' => [...], 'cascadingsources' => [...], 'int' => [...], 'special' => [...], 'speciale' => [...], 'tag' => [...], 'formatdate' => [...], 'displaytitle' => [...]]; private $mFunctionSynonyms = [0 => [...], 1 => [...]]; private $mStripList = [0 => 'pre', 1 => 'nowiki', 2 => 'gallery', 3 => 'indicator', 4 => 'langconvert', 5 => 'math', 6 => 'chem', 7 => 'source', 8 => 'syntaxhighlight', 9 => 'ref', 10 => 'references']; private $mVarCache = []; private $mImageParams = []; private $mImageParamsMagicArray = []; public $mMarkerIndex = 1; private $mVariables = class MagicWordArray { public $names = [...]; private $factory = class MagicWordFactory { ... }; private $hash = [...]; private $baseRegex = NULL; private $regex = NULL }; private $mSubstWords = class MagicWordArray { public $names = [...]; private $factory = class MagicWordFactory { ... }; private $hash = NULL; private $baseRegex = [...]; private $regex = NULL }; private $mExtLinkBracketedRegex = '/\\[(((?i)bitcoin\\:\|ftp\\:\\/\\/\|ftps\\:\\/\\/\|geo\\:\|git\\:\\/\\/\|gopher\\:\\/\\/\|http\\:\\/\\/\|https\\:\\/\\/\|irc\\:\\/\\/\|ircs\\:\\/\\/\|magnet\\:\|mailto\\:\|matrix\\:\|mms\\:\\/\\/\|news\\:\|nntp\\:\\/\\/\|redis\\:\\/\\/\|sftp\\:\\/\\/\|sip\\:\|sips\\:\|sms\\:\|ssh\\:\\/\\/\|svn\\:\\/\\/\|tel\\:\|telnet\\:\\/\\/\|urn\\:\|worldwind\\:\\/\\/\|xmpp\\:\|\\/\\/)(?:[0-9.]+\|\\[(?i:[0-9a-f:.]+)\\]\|[^][<>"\\x00-\\x20\\x7F\\p{Zs}\\x{FFFD}])[^][<>"\\x00-\\x20\\x7F\\p{Zs}\\x{FFFD}])\\p{Zs}([^\\]\\x00-\\x08\\x0a-\\x1F\\x{FFFD}]?)\\]/Su'; private $urlUtils = class MediaWiki\Utils\UrlUtils { private $server = 'https://wiki.math.wisc.edu'; private $canonicalServer = 'https://wiki.math.wisc.edu'; private $internalServer = 'https://wiki.math.wisc.edu'; private $fallbackProtocol = 'http'; private $httpsPort = 443; private $validProtocols = [...]; private $validProtocolsCache = 'bitcoin\\:\|ftp\\:\\/\\/\|ftps\\:\\/\\/\|geo\\:\|git\\:\\/\\/\|gopher\\:\\/\\/\|http\\:\\/\\/\|https\\:\\/\\/\|irc\\:\\/\\/\|ircs\\:\\/\\/\|magnet\\:\|mailto\\:\|matrix\\:\|mms\\:\\/\\/\|news\\:\|nntp\\:\\/\\/\|redis\\:\\/\\/\|sftp\\:\\/\\/\|sip\\:\|sips\\:\|sms\\:\|ssh\\:\\/\\/\|svn\\:\\/\\/\|tel\\:\|telnet\\:\\/\\/\|urn\\:\|worldwind\\:\\/\\/\|xmpp\\:\|\\/\\/'; private $validAbsoluteProtocolsCache = 'bitcoin\\:\|ftp\\:\\/\\/\|ftps\\:\\/\\/\|geo\\:\|git\\:\\/\\/\|gopher\\:\\/\\/\|http\\:\\/\\/\|https\\:\\/\\/\|irc\\:\\/\\/\|ircs\\:\\/\\/\|magnet\\:\|mailto\\:\|matrix\\:\|mms\\:\\/\\/\|news\\:\|nntp\\:\\/\\/\|redis\\:\\/\\/\|sftp\\:\\/\\/\|sip\\:\|sips\\:\|sms\\:\|ssh\\:\\/\\/\|svn\\:\\/\\/\|tel\\:\|telnet\\:\\/\\/\|urn\\:\|worldwind\\:\\/\\/\|xmpp\\:' }; private $mPreprocessor = class Preprocessor_Hash { public $parser = ...; protected $wanCache = class WANObjectCache { ... }; protected $disableLangConversion = FALSE; protected $rules = [...]; protected $cacheThreshold = 1000 }; private $mOutput = class ParserOutput { protected $mParseUsedOptions = [...]; protected $mCacheTime = ''; protected $mCacheExpiry = NULL; protected $mCacheRevisionId = NULL; private $mText = NULL; private $mLanguageLinks = [...]; private $mCategories = [...]; private $mIndicators = [...]; private $mTitleText = ''; private $mLinks = [...]; private $mLinksSpecial = [...]; private $mTemplates = [...]; private $mTemplateIds = [...]; private $mImages = [...]; private $mFileSearchOptions = [...]; private $mExternalLinks = [...]; private $mInterwikiLinks = [...]; private $mNewSection = FALSE; private $mHideNewSection = FALSE; private $mNoGallery = FALSE; private $mHeadItems = [...]; private $mModules = [...]; private $mModuleStyles = [...]; private $mJsConfigVars = [...]; private $mOutputHooks = [...]; private $mWarnings = [...]; private $mWarningMsgs = [...]; private $mSections = [...]; private $mProperties = [...]; private $mTOCHTML = ''; private $mTimestamp = NULL; private $mEnableOOUI = FALSE; private $mIndexSet = FALSE; private $mNoIndexSet = FALSE; private $mExtensionData = [...]; private $mLimitReportData = [...]; private $mLimitReportJSData = [...]; private $mCacheMessage = ''; private $mParseStartTime = [...]; private $mPreventClickjacking = FALSE; private $mExtraScriptSrcs = [...]; private $mExtraDefaultSrcs = [...]; private $mExtraStyleSrcs = [...]; private $mFlags = [...]; private $mSpeculativeRevId = NULL; private $speculativePageIdUsed = NULL; private $revisionTimestampUsed = NULL; private $revisionUsedSha1Base36 = NULL; private $mWrapperDivClasses = [...]; private $mMaxAdaptiveExpiry = INF }; private $mAutonumber = 0; private $mStripState = class StripState { protected $data = [...]; protected $regex = '/\'"`UNIQ-([^<>&\'"]+)-QINU`"\'/'; protected $parser = ...; protected $circularRefGuard = [...]; protected $depth = 0; protected $highestDepth = 0; protected $expandSize = 0; protected $depthLimit = 20; protected $sizeLimit = 5000000 }; private $mLinkHolders = class LinkHolderArray { public $internals = [...]; public $interwikis = [...]; public $size = 0; public $parent = ...; private $languageConverter = class TrivialLanguageConverter { ... }; private $hookRunner = class MediaWiki\HookContainer\HookRunner { ... } }; private $mLinkID = 0; private $mIncludeSizes = ['post-expand' => 0, 'arg' => 0]; public $mPPNodeCount = 6; public $mHighestExpansionDepth = 2; private $mTplRedirCache = []; public $mHeadings = [0 => [...], 1 => [...]]; private $mDoubleUnderscores = []; public $mExpensiveFunctionCount = 0; private $mShowToc = TRUE; private $mForceTocPosition = FALSE; private $mTplDomCache = []; private $mUser = NULL; public $mOptions = class ParserOptions { private $options = [...]; private $mTimestamp = NULL; private $mUser = class User { ... }; private $onAccessCallback = [...]; private $redirectTarget = NULL; private $mExtraKey = '' }; public $mTitle = class Title { private $mTextform = 'Past Probability Seminars Spring 2020'; private $mUrlform = 'Past_Probability_Seminars_Spring_2020'; private $mDbkeyform = 'Past_Probability_Seminars_Spring_2020'; private $mNamespace = 0; private $mInterwiki = ''; private $mLocalInterwiki = FALSE; private $mFragment = ''; public $mArticleID = 92; protected $mLatestID = FALSE; private $mContentModel = FALSE; private $mForcedContentModel = FALSE; private $mEstimateRevisions = NULL; public $prefixedText = NULL; protected $mLength = -1; public $mRedirect = NULL; private $mHasSubpages = NULL; private $mPageLanguage = NULL; private $mDbPageLanguage = FALSE; private $mTitleValue = NULL; private $mIsBigDeletion = NULL; private $mIsValid = NULL; private $mInstanceCacheKey = NULL; protected $deprecatedPublicProperties = [...]; private $dynamicPropertiesAccessDeprecated = FALSE }; private $mOutputType = 1; public $ot = ['html' => TRUE, 'wiki' => FALSE, 'pre' => FALSE, 'plain' => FALSE]; private $mRevisionId = 16436; private $mRevisionTimestamp = NULL; private $mRevisionUser = NULL; private $mRevisionSize = NULL; private $mInputSize = 9476; private $mRevisionRecordObject = NULL; private $mLangLinkLanguages = []; private $currentRevisionCache = NULL; private $mInParse = '#0 /var/www/wiki_mediawiki-1.39.3/includes/parser/Parser.php(699): Parser->lock()\n#1 /var/www/wiki_mediawiki-1.39.3/includes/content/WikitextContentHandler.php(301): Parser->parse()\n#2 /var/www/wiki_mediawiki-1.39.3/includes/content/ContentHandler.php(1720): WikitextContentHandler->fillParserOutput()\n#3 /var/www/wiki_mediawiki-1.39.3/includes/content/Renderer/ContentRenderer.php(47): ContentHandler->getParserOutput()\n#4 /var/www/wiki_mediawiki-1.39.3/includes/Revision/RenderedRevision.php(265): MediaWiki\\Co'...; private $mProfiler = class SectionProfiler { protected $start = NULL; protected $end = NULL; protected $stack = [...]; protected $workStack = [...]; protected $collated = [...]; protected $collateDone = FALSE; protected $errorEntry = [...]; protected $logger = class MediaWiki\Logger\LegacyLogger { ... } }; private $mLinkRenderer = NULL; private $magicWordFactory = class MagicWordFactory { private $mVariableIDsInitialised = TRUE; private $mVariableIDs = [...]; private $mCacheTTLs = [...]; private $mDoubleUnderscoreIDs = [...]; private $mSubstIDs = [...]; private $mObjects = [...]; private $mDoubleUnderscoreArray = class MagicWordArray { ... }; private $contLang = class LanguageEn { ... }; private $hookRunner = class MediaWiki\HookContainer\HookRunner { ... } }; private $contLang = class LanguageEn { public $mCode = 'en'; public $mMagicExtensions = [...]; private ${Language}mHtmlCode = NULL; public $dateFormatStrings = [...]; public $mExtendedSpecialPageAliases = [...]; protected $namespaceNames = [...]; protected $mNamespaceIds = NULL; protected $namespaceAliases = NULL; private ${Language}transformData = [...]; private ${Language}namespaceInfo = class NamespaceInfo { ... }; private ${Language}localisationCache = class LocalisationCache { ... }; private ${Language}langNameUtils = class MediaWiki\Languages\LanguageNameUtils { ... }; private ${Language}langFallback = class MediaWiki\Languages\LanguageFallback { ... }; private ${Language}grammarTransformCache = NULL; private ${Language}converterFactory = class MediaWiki\Languages\LanguageConverterFactory { ... }; private ${Language}hookContainer = class MediaWiki\HookContainer\HookContainer { ... }; private ${Language}hookRunner = class MediaWiki\HookContainer\HookRunner { ... }; private ${Language}config = class GlobalVarConfig { ... } }; private $languageConverterFactory = class MediaWiki\Languages\LanguageConverterFactory { private $cache = [...]; private $converterList = [...]; private $objectFactory = class Wikimedia\ObjectFactory\ObjectFactory { ... }; private $isConversionDisabled = FALSE; private $isTitleConversionDisabled = FALSE; private $defaultLanguage = class Closure { ... } }; private $factory = class ParserFactory { private $svcOptions = class MediaWiki\Config\ServiceOptions { ... }; private $magicWordFactory = class MagicWordFactory { ... }; private $contLang = class LanguageEn { ... }; private $urlUtils = class MediaWiki\Utils\UrlUtils { ... }; private $specialPageFactory = class MediaWiki\SpecialPage\SpecialPageFactory { ... }; private $linkRendererFactory = class MediaWiki\Linker\LinkRendererFactory { ... }; private $nsInfo = class NamespaceInfo { ... }; private $logger = class MediaWiki\Logger\LegacyLogger { ... }; private $badFileLookup = class MediaWiki\BadFileLookup { ... }; private $languageConverterFactory = class MediaWiki\Languages\LanguageConverterFactory { ... }; private $userOptionsLookup = class MediaWiki\User\UserOptionsManager { ... }; private $userFactory = class MediaWiki\User\UserFactory { ... }; private $titleFormatter = class MediaWikiTitleCodec { ... }; private $httpRequestFactory = class MediaWiki\Http\HttpRequestFactory { ... }; private $trackingCategories = class TrackingCategories { ... }; private $signatureValidatorFactory = class MediaWiki\Preferences\SignatureValidatorFactory { ... }; private $userNameUtils = class MediaWiki\User\UserNameUtils { ... }; private $hookContainer = class MediaWiki\HookContainer\HookContainer { ... }; private $tidy = class MediaWiki\Tidy\RemexDriver { ... }; private $wanCache = class WANObjectCache { ... }; private $mainInstance = ... }; private $specialPageFactory = class MediaWiki\SpecialPage\SpecialPageFactory { private $list = [...]; private $aliases = [...]; private $options = class MediaWiki\Config\ServiceOptions { ... }; private $contLang = class LanguageEn { ... }; private $objectFactory = class Wikimedia\ObjectFactory\ObjectFactory { ... }; private $hookContainer = class MediaWiki\HookContainer\HookContainer { ... }; private $hookRunner = class MediaWiki\HookContainer\HookRunner { ... }; private $titleFactory = class TitleFactory { ... } }; private $titleFormatter = class MediaWikiTitleCodec { protected $language = class LanguageEn { ... }; protected $genderCache = class GenderCache { ... }; protected $localInterwikis = [...]; protected $interwikiLookup = class MediaWiki\Interwiki\ClassicInterwikiLookup { ... }; protected $nsInfo = class NamespaceInfo { ... }; private $createMalformedTitleException = class Closure { ... } }; private $svcOptions = class MediaWiki\Config\ServiceOptions { private $keys = [...]; private $options = [...] }; private $linkRendererFactory = class MediaWiki\Linker\LinkRendererFactory { private $titleFormatter = class MediaWikiTitleCodec { ... }; private $linkCache = class LinkCache { ... }; private $hookContainer = class MediaWiki\HookContainer\HookContainer { ... }; private $specialPageFactory = class MediaWiki\SpecialPage\SpecialPageFactory { ... } }; private $nsInfo = class NamespaceInfo { private $alwaysCapitalizedNamespaces = [...]; private $canonicalNamespaces = [...]; private $namespaceIndexes = [...]; private $validNamespaces = [...]; private $options = class MediaWiki\Config\ServiceOptions { ... }; private $hookRunner = class MediaWiki\HookContainer\HookRunner { ... } }; private $logger = class MediaWiki\Logger\LegacyLogger { protected $channel = 'Parser'; private $minimumLevel = 999; private $isDB = FALSE }; private $badFileLookup = class MediaWiki\BadFileLookup { private $listCallback = class Closure { ... }; private $cache = class EmptyBagOStuff { ... }; private $repoGroup = class RepoGroup { ... }; private $titleParser = class MediaWikiTitleCodec { ... }; private $badFiles = NULL; private $hookRunner = class MediaWiki\HookContainer\HookRunner { ... } }; private $hookContainer = class MediaWiki\HookContainer\HookContainer { private $dynamicHandlers = [...]; private $tombstones = [...]; private $handlersByName = [...]; private $registry = class MediaWiki\HookContainer\GlobalHookRegistry { ... }; private $objectFactory = class Wikimedia\ObjectFactory\ObjectFactory { ... }; private $nextScopedRegisterId = 0 }; private $hookRunner = class MediaWiki\HookContainer\HookRunner { private $container = class MediaWiki\HookContainer\HookContainer { ... } }; private $tidy = class MediaWiki\Tidy\RemexDriver { protected $config = [...]; private $treeMutationTrace = FALSE; private $serializerTrace = FALSE; private $mungerTrace = FALSE; private $pwrap = TRUE; private $enableLegacyMediaDOM = TRUE }; private $userOptionsLookup = class MediaWiki\User\UserOptionsManager { private $serviceOptions = class MediaWiki\Config\ServiceOptions { ... }; private $defaultOptionsLookup = class MediaWiki\User\DefaultOptionsLookup { ... }; private $languageConverterFactory = class MediaWiki\Languages\LanguageConverterFactory { ... }; private $loadBalancer = class Wikimedia\Rdbms\LoadBalancer { ... }; private $userFactory = class MediaWiki\User\UserFactory { ... }; private $logger = class MediaWiki\Logger\LegacyLogger { ... }; private $modifiedOptions = [...]; private $originalOptionsCache = [...]; private $optionsFromDb = [...]; private $hookRunner = class MediaWiki\HookContainer\HookRunner { ... }; private $queryFlagsUsedForCaching = [...] }; private $userFactory = class MediaWiki\User\UserFactory { private $loadBalancer = class Wikimedia\Rdbms\LoadBalancer { ... }; private $userNameUtils = class MediaWiki\User\UserNameUtils { ... }; private $lastUserFromIdentity = NULL }; private $httpRequestFactory = class MediaWiki\Http\HttpRequestFactory { private $options = class MediaWiki\Config\ServiceOptions { ... }; private $logger = class MediaWiki\Logger\LegacyLogger { ... } }; private $trackingCategories = class TrackingCategories { private $options = class MediaWiki\Config\ServiceOptions { ... }; private $namespaceInfo = class NamespaceInfo { ... }; private $titleParser = class MediaWikiTitleCodec { ... }; private $extensionRegistry = class ExtensionRegistry { ... }; private $logger = class MediaWiki\Logger\LegacyLogger { ... } }; private $signatureValidatorFactory = class MediaWiki\Preferences\SignatureValidatorFactory { private $serviceOptions = class MediaWiki\Config\ServiceOptions { ... }; private $parserFactoryClosure = class Closure { ... }; private $specialPageFactory = class MediaWiki\SpecialPage\SpecialPageFactory { ... }; private $titleFactory = class TitleFactory { ... } }; private $userNameUtils = class MediaWiki\User\UserNameUtils { private $options = class MediaWiki\Config\ServiceOptions { ... }; private $contentLang = class LanguageEn { ... }; private $logger = class MediaWiki\Logger\LegacyLogger { ... }; private $titleParser = class MediaWikiTitleCodec { ... }; private $textFormatter = class MediaWiki\Message\TextFormatter { ... }; private $reservedUsernames = FALSE; private $hookRunner = class MediaWiki\HookContainer\HookRunner { ... }; private $tempUserConfig = class MediaWiki\User\TempUser\RealTempUserConfig { ... } }; protected $deprecatedPublicProperties = ['mLinkID' => [...], 'mIncludeSizes' => [...], 'mDoubleUnderscores' => [...], 'mShowToc' => [...], 'mRevisionId' => [...], 'mRevisionTimestamp' => [...], 'mRevisionUser' => [...], 'mRevisionSize' => [...], 'mInputSize' => [...], 'mInParse' => [...], 'mFirstCall' => [...], 'mGeneratedPPNodeCount' => [...]]; private $dynamicPropertiesAccessDeprecated = FALSE }, $frame = class PPFrame_Hash { public $parser = class Parser { private $mTagHooks = [...]; private $mFunctionHooks = [...]; private $mFunctionSynonyms = [...]; private $mStripList = [...]; private $mVarCache = [...]; private $mImageParams = [...]; private $mImageParamsMagicArray = [...]; public $mMarkerIndex = 1; private $mVariables = class MagicWordArray { ... }; private $mSubstWords = class MagicWordArray { ... }; private $mExtLinkBracketedRegex = '/\\[(((?i)bitcoin\\:\|ftp\\:\\/\\/\|ftps\\:\\/\\/\|geo\\:\|git\\:\\/\\/\|gopher\\:\\/\\/\|http\\:\\/\\/\|https\\:\\/\\/\|irc\\:\\/\\/\|ircs\\:\\/\\/\|magnet\\:\|mailto\\:\|matrix\\:\|mms\\:\\/\\/\|news\\:\|nntp\\:\\/\\/\|redis\\:\\/\\/\|sftp\\:\\/\\/\|sip\\:\|sips\\:\|sms\\:\|ssh\\:\\/\\/\|svn\\:\\/\\/\|tel\\:\|telnet\\:\\/\\/\|urn\\:\|worldwind\\:\\/\\/\|xmpp\\:\|\\/\\/)(?:[0-9.]+\|\\[(?i:[0-9a-f:.]+)\\]\|[^][<>"\\x00-\\x20\\x7F\\p{Zs}\\x{FFFD}])[^][<>"\\x00-\\x20\\x7F\\p{Zs}\\x{FFFD}])\\p{Zs}([^\\]\\x00-\\x08\\x0a-\\x1F\\x{FFFD}]?)\\]/Su'; private $urlUtils = class MediaWiki\Utils\UrlUtils { ... }; private $mPreprocessor = class Preprocessor_Hash { ... }; private $mOutput = class ParserOutput { ... }; private $mAutonumber = 0; private $mStripState = class StripState { ... }; private $mLinkHolders = class LinkHolderArray { ... }; private $mLinkID = 0; private $mIncludeSizes = [...]; public $mPPNodeCount = 6; public $mHighestExpansionDepth = 2; private $mTplRedirCache = [...]; public $mHeadings = [...]; private $mDoubleUnderscores = [...]; public $mExpensiveFunctionCount = 0; private $mShowToc = TRUE; private $mForceTocPosition = FALSE; private $mTplDomCache = [...]; private $mUser = NULL; public $mOptions = class ParserOptions { ... }; public $mTitle = class Title { ... }; private $mOutputType = 1; public $ot = [...]; private $mRevisionId = 16436; private $mRevisionTimestamp = NULL; private $mRevisionUser = NULL; private $mRevisionSize = NULL; private $mInputSize = 9476; private $mRevisionRecordObject = NULL; private $mLangLinkLanguages = [...]; private $currentRevisionCache = NULL; private $mInParse = '#0 /var/www/wiki_mediawiki-1.39.3/includes/parser/Parser.php(699): Parser->lock()\n#1 /var/www/wiki_mediawiki-1.39.3/includes/content/WikitextContentHandler.php(301): Parser->parse()\n#2 /var/www/wiki_mediawiki-1.39.3/includes/content/ContentHandler.php(1720): WikitextContentHandler->fillParserOutput()\n#3 /var/www/wiki_mediawiki-1.39.3/includes/content/Renderer/ContentRenderer.php(47): ContentHandler->getParserOutput()\n#4 /var/www/wiki_mediawiki-1.39.3/includes/Revision/RenderedRevision.php(265): MediaWiki\\Co'...; private $mProfiler = class SectionProfiler { ... }; private $mLinkRenderer = NULL; private $magicWordFactory = class MagicWordFactory { ... }; private $contLang = class LanguageEn { ... }; private $languageConverterFactory = class MediaWiki\Languages\LanguageConverterFactory { ... }; private $factory = class ParserFactory { ... }; private $specialPageFactory = class MediaWiki\SpecialPage\SpecialPageFactory { ... }; private $titleFormatter = class MediaWikiTitleCodec { ... }; private $svcOptions = class MediaWiki\Config\ServiceOptions { ... }; private $linkRendererFactory = class MediaWiki\Linker\LinkRendererFactory { ... }; private $nsInfo = class NamespaceInfo { ... }; private $logger = class MediaWiki\Logger\LegacyLogger { ... }; private $badFileLookup = class MediaWiki\BadFileLookup { ... }; private $hookContainer = class MediaWiki\HookContainer\HookContainer { ... }; private $hookRunner = class MediaWiki\HookContainer\HookRunner { ... }; private $tidy = class MediaWiki\Tidy\RemexDriver { ... }; private $userOptionsLookup = class MediaWiki\User\UserOptionsManager { ... }; private $userFactory = class MediaWiki\User\UserFactory { ... }; private $httpRequestFactory = class MediaWiki\Http\HttpRequestFactory { ... }; private $trackingCategories = class TrackingCategories { ... }; private $signatureValidatorFactory = class MediaWiki\Preferences\SignatureValidatorFactory { ... }; private $userNameUtils = class MediaWiki\User\UserNameUtils { ... }; protected $deprecatedPublicProperties = [...]; private $dynamicPropertiesAccessDeprecated = FALSE }; public $preprocessor = class Preprocessor_Hash { public $parser = class Parser { ... }; protected $wanCache = class WANObjectCache { ... }; protected $disableLangConversion = FALSE; protected $rules = [...]; protected $cacheThreshold = 1000 }; public $title = class Title { private $mTextform = 'Past Probability Seminars Spring 2020'; private $mUrlform = 'Past_Probability_Seminars_Spring_2020'; private $mDbkeyform = 'Past_Probability_Seminars_Spring_2020'; private $mNamespace = 0; private $mInterwiki = ''; private $mLocalInterwiki = FALSE; private $mFragment = ''; public $mArticleID = 92; protected $mLatestID = FALSE; private $mContentModel = FALSE; private $mForcedContentModel = FALSE; private $mEstimateRevisions = NULL; public $prefixedText = NULL; protected $mLength = -1; public $mRedirect = NULL; private $mHasSubpages = NULL; private $mPageLanguage = NULL; private $mDbPageLanguage = FALSE; private $mTitleValue = NULL; private $mIsBigDeletion = NULL; private $mIsValid = NULL; private $mInstanceCacheKey = NULL; protected $deprecatedPublicProperties = [...]; private $dynamicPropertiesAccessDeprecated = FALSE }; public $titleCache = [0 => 'Past_Probability_Seminars_Spring_2020']; public $loopCheckHash = []; public $depth = 0; private $volatile = FALSE; private $ttl = NULL; protected $childExpansionCache = []; private $maxPPNodeCount = 1000000; private $maxPPExpandDepth = 100 } )	.../Parser.php:4023
29	0.1258	2517480	SimpleMathJaxHooks::renderTex( $tex = '\\displaystyle{ d }', $parser = class Parser { private $mTagHooks = ['pre' => [...], 'nowiki' => [...], 'gallery' => [...], 'indicator' => [...], 'langconvert' => [...], 'math' => 'SimpleMathJaxHooks::renderMath', 'chem' => 'SimpleMathJaxHooks::renderChem', 'source' => [...], 'syntaxhighlight' => [...], 'ref' => [...], 'references' => [...]]; private $mFunctionHooks = ['ns' => [...], 'nse' => [...], 'urlencode' => [...], 'lcfirst' => [...], 'ucfirst' => [...], 'lc' => [...], 'uc' => [...], 'localurl' => [...], 'localurle' => [...], 'fullurl' => [...], 'fullurle' => [...], 'canonicalurl' => [...], 'canonicalurle' => [...], 'formatnum' => [...], 'grammar' => [...], 'gender' => [...], 'plural' => [...], 'bidi' => [...], 'numberofpages' => [...], 'numberofusers' => [...], 'numberofactiveusers' => [...], 'numberofarticles' => [...], 'numberoffiles' => [...], 'numberofadmins' => [...], 'numberingroup' => [...], 'numberofedits' => [...], 'language' => [...], 'padleft' => [...], 'padright' => [...], 'anchorencode' => [...], 'defaultsort' => [...], 'filepath' => [...], 'pagesincategory' => [...], 'pagesize' => [...], 'protectionlevel' => [...], 'protectionexpiry' => [...], 'namespace' => [...], 'namespacee' => [...], 'namespacenumber' => [...], 'talkspace' => [...], 'talkspacee' => [...], 'subjectspace' => [...], 'subjectspacee' => [...], 'pagename' => [...], 'pagenamee' => [...], 'fullpagename' => [...], 'fullpagenamee' => [...], 'rootpagename' => [...], 'rootpagenamee' => [...], 'basepagename' => [...], 'basepagenamee' => [...], 'subpagename' => [...], 'subpagenamee' => [...], 'talkpagename' => [...], 'talkpagenamee' => [...], 'subjectpagename' => [...], 'subjectpagenamee' => [...], 'pageid' => [...], 'revisionid' => [...], 'revisionday' => [...], 'revisionday2' => [...], 'revisionmonth' => [...], 'revisionmonth1' => [...], 'revisionyear' => [...], 'revisiontimestamp' => [...], 'revisionuser' => [...], 'cascadingsources' => [...], 'int' => [...], 'special' => [...], 'speciale' => [...], 'tag' => [...], 'formatdate' => [...], 'displaytitle' => [...]]; private $mFunctionSynonyms = [0 => [...], 1 => [...]]; private $mStripList = [0 => 'pre', 1 => 'nowiki', 2 => 'gallery', 3 => 'indicator', 4 => 'langconvert', 5 => 'math', 6 => 'chem', 7 => 'source', 8 => 'syntaxhighlight', 9 => 'ref', 10 => 'references']; private $mVarCache = []; private $mImageParams = []; private $mImageParamsMagicArray = []; public $mMarkerIndex = 1; private $mVariables = class MagicWordArray { public $names = [...]; private $factory = class MagicWordFactory { ... }; private $hash = [...]; private $baseRegex = NULL; private $regex = NULL }; private $mSubstWords = class MagicWordArray { public $names = [...]; private $factory = class MagicWordFactory { ... }; private $hash = NULL; private $baseRegex = [...]; private $regex = NULL }; private $mExtLinkBracketedRegex = '/\\[(((?i)bitcoin\\:\|ftp\\:\\/\\/\|ftps\\:\\/\\/\|geo\\:\|git\\:\\/\\/\|gopher\\:\\/\\/\|http\\:\\/\\/\|https\\:\\/\\/\|irc\\:\\/\\/\|ircs\\:\\/\\/\|magnet\\:\|mailto\\:\|matrix\\:\|mms\\:\\/\\/\|news\\:\|nntp\\:\\/\\/\|redis\\:\\/\\/\|sftp\\:\\/\\/\|sip\\:\|sips\\:\|sms\\:\|ssh\\:\\/\\/\|svn\\:\\/\\/\|tel\\:\|telnet\\:\\/\\/\|urn\\:\|worldwind\\:\\/\\/\|xmpp\\:\|\\/\\/)(?:[0-9.]+\|\\[(?i:[0-9a-f:.]+)\\]\|[^][<>"\\x00-\\x20\\x7F\\p{Zs}\\x{FFFD}])[^][<>"\\x00-\\x20\\x7F\\p{Zs}\\x{FFFD}])\\p{Zs}([^\\]\\x00-\\x08\\x0a-\\x1F\\x{FFFD}]*?)\\]/Su'; private $urlUtils = class MediaWiki\Utils\UrlUtils { private $server = 'https://wiki.math.wisc.edu'; private $canonicalServer = 'https://wiki.math.wisc.edu'; private $internalServer = 'https://wiki.math.wisc.edu'; private $fallbackProtocol = 'http'; private $httpsPort = 443; private $validProtocols = [...]; private $validProtocolsCache = 'bitcoin\\:\|ftp\\:\\/\\/\|ftps\\:\\/\\/\|geo\\:\|git\\:\\/\\/\|gopher\\:\\/\\/\|http\\:\\/\\/\|https\\:\\/\\/\|irc\\:\\/\\/\|ircs\\:\\/\\/\|magnet\\:\|mailto\\:\|matrix\\:\|mms\\:\\/\\/\|news\\:\|nntp\\:\\/\\/\|redis\\:\\/\\/\|sftp\\:\\/\\/\|sip\\:\|sips\\:\|sms\\:\|ssh\\:\\/\\/\|svn\\:\\/\\/\|tel\\:\|telnet\\:\\/\\/\|urn\\:\|worldwind\\:\\/\\/\|xmpp\\:\|\\/\\/'; private $validAbsoluteProtocolsCache = 'bitcoin\\:\|ftp\\:\\/\\/\|ftps\\:\\/\\/\|geo\\:\|git\\:\\/\\/\|gopher\\:\\/\\/\|http\\:\\/\\/\|https\\:\\/\\/\|irc\\:\\/\\/\|ircs\\:\\/\\/\|magnet\\:\|mailto\\:\|matrix\\:\|mms\\:\\/\\/\|news\\:\|nntp\\:\\/\\/\|redis\\:\\/\\/\|sftp\\:\\/\\/\|sip\\:\|sips\\:\|sms\\:\|ssh\\:\\/\\/\|svn\\:\\/\\/\|tel\\:\|telnet\\:\\/\\/\|urn\\:\|worldwind\\:\\/\\/\|xmpp\\:' }; private $mPreprocessor = class Preprocessor_Hash { public $parser = ...; protected $wanCache = class WANObjectCache { ... }; protected $disableLangConversion = FALSE; protected $rules = [...]; protected $cacheThreshold = 1000 }; private $mOutput = class ParserOutput { protected $mParseUsedOptions = [...]; protected $mCacheTime = ''; protected $mCacheExpiry = NULL; protected $mCacheRevisionId = NULL; private $mText = NULL; private $mLanguageLinks = [...]; private $mCategories = [...]; private $mIndicators = [...]; private $mTitleText = ''; private $mLinks = [...]; private $mLinksSpecial = [...]; private $mTemplates = [...]; private $mTemplateIds = [...]; private $mImages = [...]; private $mFileSearchOptions = [...]; private $mExternalLinks = [...]; private $mInterwikiLinks = [...]; private $mNewSection = FALSE; private $mHideNewSection = FALSE; private $mNoGallery = FALSE; private $mHeadItems = [...]; private $mModules = [...]; private $mModuleStyles = [...]; private $mJsConfigVars = [...]; private $mOutputHooks = [...]; private $mWarnings = [...]; private $mWarningMsgs = [...]; private $mSections = [...]; private $mProperties = [...]; private $mTOCHTML = ''; private $mTimestamp = NULL; private $mEnableOOUI = FALSE; private $mIndexSet = FALSE; private $mNoIndexSet = FALSE; private $mExtensionData = [...]; private $mLimitReportData = [...]; private $mLimitReportJSData = [...]; private $mCacheMessage = ''; private $mParseStartTime = [...]; private $mPreventClickjacking = FALSE; private $mExtraScriptSrcs = [...]; private $mExtraDefaultSrcs = [...]; private $mExtraStyleSrcs = [...]; private $mFlags = [...]; private $mSpeculativeRevId = NULL; private $speculativePageIdUsed = NULL; private $revisionTimestampUsed = NULL; private $revisionUsedSha1Base36 = NULL; private $mWrapperDivClasses = [...]; private $mMaxAdaptiveExpiry = INF }; private $mAutonumber = 0; private $mStripState = class StripState { protected $data = [...]; protected $regex = '/\'"`UNIQ-([^<>&\'"]+)-QINU`"\'/'; protected $parser = ...; protected $circularRefGuard = [...]; protected $depth = 0; protected $highestDepth = 0; protected $expandSize = 0; protected $depthLimit = 20; protected $sizeLimit = 5000000 }; private $mLinkHolders = class LinkHolderArray { public $internals = [...]; public $interwikis = [...]; public $size = 0; public $parent = ...; private $languageConverter = class TrivialLanguageConverter { ... }; private $hookRunner = class MediaWiki\HookContainer\HookRunner { ... } }; private $mLinkID = 0; private $mIncludeSizes = ['post-expand' => 0, 'arg' => 0]; public $mPPNodeCount = 6; public $mHighestExpansionDepth = 2; private $mTplRedirCache = []; public $mHeadings = [0 => [...], 1 => [...]]; private $mDoubleUnderscores = []; public $mExpensiveFunctionCount = 0; private $mShowToc = TRUE; private $mForceTocPosition = FALSE; private $mTplDomCache = []; private $mUser = NULL; public $mOptions = class ParserOptions { private $options = [...]; private $mTimestamp = NULL; private $mUser = class User { ... }; private $onAccessCallback = [...]; private $redirectTarget = NULL; private $mExtraKey = '' }; public $mTitle = class Title { private $mTextform = 'Past Probability Seminars Spring 2020'; private $mUrlform = 'Past_Probability_Seminars_Spring_2020'; private $mDbkeyform = 'Past_Probability_Seminars_Spring_2020'; private $mNamespace = 0; private $mInterwiki = ''; private $mLocalInterwiki = FALSE; private $mFragment = ''; public $mArticleID = 92; protected $mLatestID = FALSE; private $mContentModel = FALSE; private $mForcedContentModel = FALSE; private $mEstimateRevisions = NULL; public $prefixedText = NULL; protected $mLength = -1; public $mRedirect = NULL; private $mHasSubpages = NULL; private $mPageLanguage = NULL; private $mDbPageLanguage = FALSE; private $mTitleValue = NULL; private $mIsBigDeletion = NULL; private $mIsValid = NULL; private $mInstanceCacheKey = NULL; protected $deprecatedPublicProperties = [...]; private $dynamicPropertiesAccessDeprecated = FALSE }; private $mOutputType = 1; public $ot = ['html' => TRUE, 'wiki' => FALSE, 'pre' => FALSE, 'plain' => FALSE]; private $mRevisionId = 16436; private $mRevisionTimestamp = NULL; private $mRevisionUser = NULL; private $mRevisionSize = NULL; private $mInputSize = 9476; private $mRevisionRecordObject = NULL; private $mLangLinkLanguages = []; private $currentRevisionCache = NULL; private $mInParse = '#0 /var/www/wiki_mediawiki-1.39.3/includes/parser/Parser.php(699): Parser->lock()\n#1 /var/www/wiki_mediawiki-1.39.3/includes/content/WikitextContentHandler.php(301): Parser->parse()\n#2 /var/www/wiki_mediawiki-1.39.3/includes/content/ContentHandler.php(1720): WikitextContentHandler->fillParserOutput()\n#3 /var/www/wiki_mediawiki-1.39.3/includes/content/Renderer/ContentRenderer.php(47): ContentHandler->getParserOutput()\n#4 /var/www/wiki_mediawiki-1.39.3/includes/Revision/RenderedRevision.php(265): MediaWiki\\Co'...; private $mProfiler = class SectionProfiler { protected $start = NULL; protected $end = NULL; protected $stack = [...]; protected $workStack = [...]; protected $collated = [...]; protected $collateDone = FALSE; protected $errorEntry = [...]; protected $logger = class MediaWiki\Logger\LegacyLogger { ... } }; private $mLinkRenderer = NULL; private $magicWordFactory = class MagicWordFactory { private $mVariableIDsInitialised = TRUE; private $mVariableIDs = [...]; private $mCacheTTLs = [...]; private $mDoubleUnderscoreIDs = [...]; private $mSubstIDs = [...]; private $mObjects = [...]; private $mDoubleUnderscoreArray = class MagicWordArray { ... }; private $contLang = class LanguageEn { ... }; private $hookRunner = class MediaWiki\HookContainer\HookRunner { ... } }; private $contLang = class LanguageEn { public $mCode = 'en'; public $mMagicExtensions = [...]; private ${Language}mHtmlCode = NULL; public $dateFormatStrings = [...]; public $mExtendedSpecialPageAliases = [...]; protected $namespaceNames = [...]; protected $mNamespaceIds = NULL; protected $namespaceAliases = NULL; private ${Language}transformData = [...]; private ${Language}namespaceInfo = class NamespaceInfo { ... }; private ${Language}localisationCache = class LocalisationCache { ... }; private ${Language}langNameUtils = class MediaWiki\Languages\LanguageNameUtils { ... }; private ${Language}langFallback = class MediaWiki\Languages\LanguageFallback { ... }; private ${Language}grammarTransformCache = NULL; private ${Language}converterFactory = class MediaWiki\Languages\LanguageConverterFactory { ... }; private ${Language}hookContainer = class MediaWiki\HookContainer\HookContainer { ... }; private ${Language}hookRunner = class MediaWiki\HookContainer\HookRunner { ... }; private ${Language}config = class GlobalVarConfig { ... } }; private $languageConverterFactory = class MediaWiki\Languages\LanguageConverterFactory { private $cache = [...]; private $converterList = [...]; private $objectFactory = class Wikimedia\ObjectFactory\ObjectFactory { ... }; private $isConversionDisabled = FALSE; private $isTitleConversionDisabled = FALSE; private $defaultLanguage = class Closure { ... } }; private $factory = class ParserFactory { private $svcOptions = class MediaWiki\Config\ServiceOptions { ... }; private $magicWordFactory = class MagicWordFactory { ... }; private $contLang = class LanguageEn { ... }; private $urlUtils = class MediaWiki\Utils\UrlUtils { ... }; private $specialPageFactory = class MediaWiki\SpecialPage\SpecialPageFactory { ... }; private $linkRendererFactory = class MediaWiki\Linker\LinkRendererFactory { ... }; private $nsInfo = class NamespaceInfo { ... }; private $logger = class MediaWiki\Logger\LegacyLogger { ... }; private $badFileLookup = class MediaWiki\BadFileLookup { ... }; private $languageConverterFactory = class MediaWiki\Languages\LanguageConverterFactory { ... }; private $userOptionsLookup = class MediaWiki\User\UserOptionsManager { ... }; private $userFactory = class MediaWiki\User\UserFactory { ... }; private $titleFormatter = class MediaWikiTitleCodec { ... }; private $httpRequestFactory = class MediaWiki\Http\HttpRequestFactory { ... }; private $trackingCategories = class TrackingCategories { ... }; private $signatureValidatorFactory = class MediaWiki\Preferences\SignatureValidatorFactory { ... }; private $userNameUtils = class MediaWiki\User\UserNameUtils { ... }; private $hookContainer = class MediaWiki\HookContainer\HookContainer { ... }; private $tidy = class MediaWiki\Tidy\RemexDriver { ... }; private $wanCache = class WANObjectCache { ... }; private $mainInstance = ... }; private $specialPageFactory = class MediaWiki\SpecialPage\SpecialPageFactory { private $list = [...]; private $aliases = [...]; private $options = class MediaWiki\Config\ServiceOptions { ... }; private $contLang = class LanguageEn { ... }; private $objectFactory = class Wikimedia\ObjectFactory\ObjectFactory { ... }; private $hookContainer = class MediaWiki\HookContainer\HookContainer { ... }; private $hookRunner = class MediaWiki\HookContainer\HookRunner { ... }; private $titleFactory = class TitleFactory { ... } }; private $titleFormatter = class MediaWikiTitleCodec { protected $language = class LanguageEn { ... }; protected $genderCache = class GenderCache { ... }; protected $localInterwikis = [...]; protected $interwikiLookup = class MediaWiki\Interwiki\ClassicInterwikiLookup { ... }; protected $nsInfo = class NamespaceInfo { ... }; private $createMalformedTitleException = class Closure { ... } }; private $svcOptions = class MediaWiki\Config\ServiceOptions { private $keys = [...]; private $options = [...] }; private $linkRendererFactory = class MediaWiki\Linker\LinkRendererFactory { private $titleFormatter = class MediaWikiTitleCodec { ... }; private $linkCache = class LinkCache { ... }; private $hookContainer = class MediaWiki\HookContainer\HookContainer { ... }; private $specialPageFactory = class MediaWiki\SpecialPage\SpecialPageFactory { ... } }; private $nsInfo = class NamespaceInfo { private $alwaysCapitalizedNamespaces = [...]; private $canonicalNamespaces = [...]; private $namespaceIndexes = [...]; private $validNamespaces = [...]; private $options = class MediaWiki\Config\ServiceOptions { ... }; private $hookRunner = class MediaWiki\HookContainer\HookRunner { ... } }; private $logger = class MediaWiki\Logger\LegacyLogger { protected $channel = 'Parser'; private $minimumLevel = 999; private $isDB = FALSE }; private $badFileLookup = class MediaWiki\BadFileLookup { private $listCallback = class Closure { ... }; private $cache = class EmptyBagOStuff { ... }; private $repoGroup = class RepoGroup { ... }; private $titleParser = class MediaWikiTitleCodec { ... }; private $badFiles = NULL; private $hookRunner = class MediaWiki\HookContainer\HookRunner { ... } }; private $hookContainer = class MediaWiki\HookContainer\HookContainer { private $dynamicHandlers = [...]; private $tombstones = [...]; private $handlersByName = [...]; private $registry = class MediaWiki\HookContainer\GlobalHookRegistry { ... }; private $objectFactory = class Wikimedia\ObjectFactory\ObjectFactory { ... }; private $nextScopedRegisterId = 0 }; private $hookRunner = class MediaWiki\HookContainer\HookRunner { private $container = class MediaWiki\HookContainer\HookContainer { ... } }; private $tidy = class MediaWiki\Tidy\RemexDriver { protected $config = [...]; private $treeMutationTrace = FALSE; private $serializerTrace = FALSE; private $mungerTrace = FALSE; private $pwrap = TRUE; private $enableLegacyMediaDOM = TRUE }; private $userOptionsLookup = class MediaWiki\User\UserOptionsManager { private $serviceOptions = class MediaWiki\Config\ServiceOptions { ... }; private $defaultOptionsLookup = class MediaWiki\User\DefaultOptionsLookup { ... }; private $languageConverterFactory = class MediaWiki\Languages\LanguageConverterFactory { ... }; private $loadBalancer = class Wikimedia\Rdbms\LoadBalancer { ... }; private $userFactory = class MediaWiki\User\UserFactory { ... }; private $logger = class MediaWiki\Logger\LegacyLogger { ... }; private $modifiedOptions = [...]; private $originalOptionsCache = [...]; private $optionsFromDb = [...]; private $hookRunner = class MediaWiki\HookContainer\HookRunner { ... }; private $queryFlagsUsedForCaching = [...] }; private $userFactory = class MediaWiki\User\UserFactory { private $loadBalancer = class Wikimedia\Rdbms\LoadBalancer { ... }; private $userNameUtils = class MediaWiki\User\UserNameUtils { ... }; private $lastUserFromIdentity = NULL }; private $httpRequestFactory = class MediaWiki\Http\HttpRequestFactory { private $options = class MediaWiki\Config\ServiceOptions { ... }; private $logger = class MediaWiki\Logger\LegacyLogger { ... } }; private $trackingCategories = class TrackingCategories { private $options = class MediaWiki\Config\ServiceOptions { ... }; private $namespaceInfo = class NamespaceInfo { ... }; private $titleParser = class MediaWikiTitleCodec { ... }; private $extensionRegistry = class ExtensionRegistry { ... }; private $logger = class MediaWiki\Logger\LegacyLogger { ... } }; private $signatureValidatorFactory = class MediaWiki\Preferences\SignatureValidatorFactory { private $serviceOptions = class MediaWiki\Config\ServiceOptions { ... }; private $parserFactoryClosure = class Closure { ... }; private $specialPageFactory = class MediaWiki\SpecialPage\SpecialPageFactory { ... }; private $titleFactory = class TitleFactory { ... } }; private $userNameUtils = class MediaWiki\User\UserNameUtils { private $options = class MediaWiki\Config\ServiceOptions { ... }; private $contentLang = class LanguageEn { ... }; private $logger = class MediaWiki\Logger\LegacyLogger { ... }; private $titleParser = class MediaWikiTitleCodec { ... }; private $textFormatter = class MediaWiki\Message\TextFormatter { ... }; private $reservedUsernames = FALSE; private $hookRunner = class MediaWiki\HookContainer\HookRunner { ... }; private $tempUserConfig = class MediaWiki\User\TempUser\RealTempUserConfig { ... } }; protected $deprecatedPublicProperties = ['mLinkID' => [...], 'mIncludeSizes' => [...], 'mDoubleUnderscores' => [...], 'mShowToc' => [...], 'mRevisionId' => [...], 'mRevisionTimestamp' => [...], 'mRevisionUser' => [...], 'mRevisionSize' => [...], 'mInputSize' => [...], 'mInParse' => [...], 'mFirstCall' => [...], 'mGeneratedPPNodeCount' => [...]]; private $dynamicPropertiesAccessDeprecated = FALSE } )	.../SimpleMathJaxHooks.php:26
30	0.1258	2517480	ParserOutput->addModules( $modules = 'ext.SimpleMathJax' )	.../SimpleMathJaxHooks.php:34
31	0.1258	2517480	wfDeprecated( $function = 'ParserOutput::addModules with non-array argument', $version = '1.38', $component = ???, $callerOffset = ??? )	.../ParserOutput.php:1180
32	0.1258	2517480	MWDebug::deprecated( $function = 'ParserOutput::addModules with non-array argument', $version = '1.38', $component = FALSE, $callerOffset = 3 )	.../GlobalFunctions.php:765
33	0.1258	2517608	MWDebug::deprecatedMsg( $msg = 'Use of ParserOutput::addModules with non-array argument was deprecated in MediaWiki 1.38.', $version = '1.38', $component = 'MediaWiki', $callerOffset = 4 )	.../MWDebug.php:233
34	0.1258	2519304	MWDebug::sendRawDeprecated( $msg = 'Use of ParserOutput::addModules with non-array argument was deprecated in MediaWiki 1.38. [Called from SimpleMathJaxHooks::renderTex in /var/www/wiki_mediawiki-1.39.3/extensions/SimpleMathJax/SimpleMathJaxHooks.php at line 34]', $sendToLog = TRUE, $callerFunc = 'SimpleMathJaxHooks::renderTex' )	.../MWDebug.php:351
35	0.1258	2519304	trigger_error( $message = 'Use of ParserOutput::addModules with non-array argument was deprecated in MediaWiki 1.38. [Called from SimpleMathJaxHooks::renderTex in /var/www/wiki_mediawiki-1.39.3/extensions/SimpleMathJax/SimpleMathJaxHooks.php at line 34]', $error_level = 16384 )	.../MWDebug.php:381

( ! ) Warning: Cannot modify header information - headers already sent by (output started at /var/www/wiki_mediawiki-1.39.3/includes/debug/MWDebug.php:381) in /var/www/wiki_mediawiki-1.39.3/includes/WebResponse.php on line 75
Call Stack
#	Time	Memory	Function	Location
1	0.0001	357656	{main}( )	.../index.php:0
2	0.0446	1478440	wfIndexMain( )	.../index.php:46
3	0.0446	1478552	MediaWiki->run( )	.../index.php:50
4	0.0446	1478552	MediaWiki->main( )	.../MediaWiki.php:562
5	0.2035	2854512	OutputPage->output( $return = TRUE )	.../MediaWiki.php:922
6	0.2035	2871088	WebResponse->header( $string = 'Content-type: text/html; charset=UTF-8', $replace = ???, $http_response_code = ??? )	.../OutputPage.php:2825
7	0.2036	2871280	header( $header = 'Content-type: text/html; charset=UTF-8', $replace = TRUE )	.../WebResponse.php:75

( ! ) Warning: Cannot modify header information - headers already sent by (output started at /var/www/wiki_mediawiki-1.39.3/includes/debug/MWDebug.php:381) in /var/www/wiki_mediawiki-1.39.3/includes/WebResponse.php on line 75
Call Stack
#	Time	Memory	Function	Location
1	0.0001	357656	{main}( )	.../index.php:0
2	0.0446	1478440	wfIndexMain( )	.../index.php:46
3	0.0446	1478552	MediaWiki->run( )	.../index.php:50
4	0.0446	1478552	MediaWiki->main( )	.../MediaWiki.php:562
5	0.2035	2854512	OutputPage->output( $return = TRUE )	.../MediaWiki.php:922
6	0.2039	2871200	WebResponse->header( $string = 'Content-language: en', $replace = ???, $http_response_code = ??? )	.../OutputPage.php:2826
7	0.2039	2871200	header( $header = 'Content-language: en', $replace = TRUE )	.../WebResponse.php:75

( ! ) Warning: Cannot modify header information - headers already sent by (output started at /var/www/wiki_mediawiki-1.39.3/includes/debug/MWDebug.php:381) in /var/www/wiki_mediawiki-1.39.3/includes/WebResponse.php on line 75
Call Stack
#	Time	Memory	Function	Location
1	0.0001	357656	{main}( )	.../index.php:0
2	0.0446	1478440	wfIndexMain( )	.../index.php:46
3	0.0446	1478552	MediaWiki->run( )	.../index.php:50
4	0.0446	1478552	MediaWiki->main( )	.../MediaWiki.php:562
5	0.2035	2854512	OutputPage->output( $return = TRUE )	.../MediaWiki.php:922
6	0.3094	3635152	OutputPage->sendCacheControl( )	.../OutputPage.php:2891
7	0.3095	3636168	WebResponse->header( $string = 'Vary: Accept-Encoding, Cookie', $replace = ???, $http_response_code = ??? )	.../OutputPage.php:2691
8	0.3095	3636168	header( $header = 'Vary: Accept-Encoding, Cookie', $replace = TRUE )	.../WebResponse.php:75

( ! ) Warning: Cannot modify header information - headers already sent by (output started at /var/www/wiki_mediawiki-1.39.3/includes/debug/MWDebug.php:381) in /var/www/wiki_mediawiki-1.39.3/includes/WebResponse.php on line 75
Call Stack
#	Time	Memory	Function	Location
1	0.0001	357656	{main}( )	.../index.php:0
2	0.0446	1478440	wfIndexMain( )	.../index.php:46
3	0.0446	1478552	MediaWiki->run( )	.../index.php:50
4	0.0446	1478552	MediaWiki->main( )	.../MediaWiki.php:562
5	0.2035	2854512	OutputPage->output( $return = TRUE )	.../MediaWiki.php:922
6	0.3094	3635152	OutputPage->sendCacheControl( )	.../OutputPage.php:2891
7	0.3098	3652560	WebResponse->header( $string = 'Expires: Thu, 01 Jan 1970 00:00:00 GMT', $replace = ???, $http_response_code = ??? )	.../OutputPage.php:2728
8	0.3098	3652560	header( $header = 'Expires: Thu, 01 Jan 1970 00:00:00 GMT', $replace = TRUE )	.../WebResponse.php:75

Past Probability Seminars Spring 2020