Past Probability Seminars Spring 2020: Difference between revisions

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= Spring 2014 =
= Spring 2020 =


<b>Thursdays in 901 Van Vleck Hall at 2:30 PM</b>, unless otherwise noted.
<b>We  usually end for questions at 3:20 PM.</b>


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


Thursdays in 901 Van Vleck Hall at 2:25 PM, unless otherwise noted.  
== January 23, 2020, [https://www.math.wisc.edu/~seppalai/ Timo Seppalainen] (UW Madison) ==
'''Non-existence of bi-infinite geodesics in the exponential corner growth model
'''


<b>
Whether bi-infinite geodesics exist has been a significant open problem in first- and last-passage percolation since the mid-80s.  A non-existence proof  in the case of directed planar last-passage percolation with exponential weights was posted by Basu, Hoffman and Sly in  November 2018. Their proof utilizes estimates from integrable probability.    This talk describes an independent proof completed 10 months later that relies on couplings, coarse graining, and control of geodesics through planarity and increment-stationary last-passage percolation. Joint work with Marton Balazs and Ofer Busani (Bristol).
If you would like to sign up for the email list to receive seminar announcements then please send an email to[[File:probsem.jpg]]
</b>


= =
== January 30, 2020, [https://www.math.wisc.edu/people/vv-prof-directory Scott Smith] (UW Madison) ==
'''Quasi-linear parabolic equations with singular forcing'''


== Thursday, January 23, <span style="color:red"> CANCELED--NO SEMINAR </span> ==
The classical solution theory for stochastic ODE's is centered around Ito's stochastic integral.  By intertwining ideas from analysis and probability, this approach extends to many PDE's, a canonical example being multiplicative stochastic heat equations driven by space-time white noise.  In both the ODE and PDE settings, the solution theory is beyond the scope of classical deterministic theory because of the ambiguity in multiplying a function with a white noise. The theory of rough paths and regularity structures provides a more quantitative understanding of this difficulty, leading to a more refined solution theory which efficiently divides the analytic and probabilistic aspects of the problem, and remarkably, even has an algebraic component.


<!--
In this talk, we will discuss a new application of these ideas to stochastic heat equations where the strength of the diffusion is not constant but random, as it depends locally on the solution.  These are known as quasi-linear equations.  Our main result yields the deterministic side of a solution theory for these PDE's, modulo a suitable renormalization.  Along the way, we identify a formally infinite series expansion of the solution which guides our analysis, reveals a nice algebraic structure, and encodes the counter-terms in the PDE.  This is joint work with Felix Otto, Jonas Sauer, and Hendrik Weber.


[http://www.stat.berkeley.edu/~mshkolni/ Mykhaylo Shkolnikov], UC-Berkeley Stats Dept==
== February 6, 2020, [https://sites.google.com/site/cyleeken/ Cheuk-Yin Lee] (Michigan State) ==
'''Sample path properties of stochastic partial differential equations: modulus of continuity and multiple points'''


In this talk, we will discuss sample path properties of stochastic partial differential equations (SPDEs). We will present a sharp regularity result for the stochastic wave equation driven by an additive Gaussian noise that is white in time and colored in space. We prove the exact modulus of continuity via the property of local nondeterminism. We will also discuss the existence problem for multiple points (or self-intersections) of the sample paths of SPDEs. Our result shows that multiple points do not exist in the critical dimension for a large class of Gaussian random fields including the solution of a linear system of stochastic heat or wave equations.


'''Title: Intertwinings, wave equations and growth models'''
== February 13, 2020, [http://www.jelena-diakonikolas.com/ Jelena Diakonikolas] (UW Madison) ==
'''Langevin Monte Carlo Without Smoothness'''


Abstract: We will discuss a general theory of intertwined diffusion processes of any dimension. Intertwined processes arise in many different contexts in probability theory, most notably in the study of random matrices, random polymers and path decompositions of Brownian motion. Recently, they turned out to be also closely related to hyperbolic partial differential equations, symmetric polynomials and the corresponding random growth models. The talk will be devoted to these recent developments which also shed new light on some beautiful old examples of intertwinings. Based on joint works with Vadim Gorin and Soumik Pal.
Langevin Monte Carlo (LMC) is an iterative algorithm used to generate samples from a distribution that is known only up to a normalizing constant. The nonasymptotic dependence of its mixing time on the dimension and target accuracy is understood mainly in the setting of smooth (gradient-Lipschitz) log-densities, a serious limitation for applications in machine learning. We remove this limitation by providing polynomial-time convergence guarantees for a variant of LMC in the setting of non-smooth log-concave distributions. At a high level, our results follow by leveraging the implicit smoothing of the log-density that comes from a small Gaussian perturbation that we add to the iterates of the algorithm and while controlling the bias and variance that are induced by this perturbation.
-->
Based on joint work with Niladri Chatterji, Michael I. Jordan, and Peter L. Bartlett.


<!-- == Thursday, January 30, TBA == -->
== February 20, 2020, [https://math.berkeley.edu/~pmwood/ Philip Matchett Wood] (UC Berkeley) ==
'''A replacement principle for perturbations of non-normal matrices'''


== Thursday, February 6, [http://people.mbi.ohio-state.edu/newby.23/ Jay Newby], [http://mbi.osu.edu/ Mathematical Biosciences Institute]  ==
There are certain non-normal matrices whose eigenvalues can change dramatically when a small perturbation is added.  However, when that perturbation is an iid random matrix, it appears that the eigenvalues become stable after perturbation and only change slightly when further small perturbations are added. Much of the work is this situation has focused on iid random gaussian perturbations. In this talk, we will discuss work on a universality result that allows for consideration of non-gaussian perturbations, and that shows that all perturbations satisfying certain conditions will produce the same limiting eigenvalue measure. Interestingly, this even allows for deterministic perturbations to be consideredJoint work with Sean O'Rourke.


Title: Applications of large deviation theory in neuroscience
== February 27, 2020, No seminar ==
''' '''


Abstract:
== March 5, 2020, [https://www.ias.edu/scholars/jiaoyang-huang Jiaoyang Huang] (IAS) ==
The membrane voltage of a neuron is modeled with a piecewise deterministic stochastic process.  The membrane voltage changes deterministically while the population of open ion channels, which allow current to flow across the membrane, is constant.  Ion channels open and close randomly, and the transition rates depend on voltage, making the process nonlinear. In the limit of infinite transition rates, the process becomes deterministic. The deterministic process is the well known Morris-Lecar model.  Under certain conditions, the deterministic process has one stable fixed point and is excitable.  An excitable event, called an action potential, is a single large transient spike in voltage that eventually returns to the stable steady state.  I will discuss recent development of large deviation theory to study noise induced action potentials.
''' Large Deviation Principles via Spherical Integrals'''


== Thursday, February 13, [http://www.math.wisc.edu/~holcomb/ Diane Holcomb], [http://www.math.wisc.edu/ UW-Madison] ==
In this talk, I'll explain a framework to study the large deviation principle for matrix models and their quantized versions, by tilting the measures using the asymptotics of spherical integrals obtained by Guionnet and Zeitouni. As examples, we obtain


Title: Large deviations for point process limits of random matrices.
1) the large deviation principle for the empirical distribution of the diagonal entries of $UB_NU^*$, for a sequence of $N\times N$ diagonal matrices $B_N$ and unitary/orthogonal Haar distributed matrices $U$;


Abstract: The Gaussian Unitary ensemble (GUE) is one of the most studied Hermitian random matrix model. When appropriately rescaled the eigenvalues in the bulk of the spectrum converge to a translation invariant limiting point process called the Sine process. On large intervals one expects the Sine process to have a number of points that is roughly the length of the interval times a fixed constant (the density of the process). We solve the large deviation problem which asks about the asymptotic probability of seeing a different density in a large interval as the size of the interval tends to infinity. Our proof works for a one-parameter family of models called beta-ensembles which contain the Gaussian orthogonal, unitary and symplectic ensembles as special cases.
2) the large deviation upper bound for the empirical eigenvalue distribution of $A_N+UB_NU^*$, for two sequences of $N\times N$ diagonal matrices $A_N, B_N$, and their complementary lower bounds at "good" probability distributions;


== Thursday, February 20, Philip Matchett Wood, UW-Madison ==
3) the large deviation principle for the Kostka number $K_{\lambda_N \eta_N}$, for two sequences of partitions $\lambda_N, \eta_N$ with at most $N$ rows;


Title: The empirical spectral distribution (ESD) of a fixed matrix plus small random noise.
4) the large deviation upper bound for the Littlewood-Richardson coefficients $c_{\lambda_N \eta_N}^{\kappa_N}$, for three sequences of partitions $\lambda_N, \eta_N, \kappa_N$ with at most $N$ rows, and their complementary lower bounds at "good" probability distributions.
 
Abstract: A fixed matrix has a distribution of eigenvalues in the complex
plane.  Small random noise can be formed by a random matrix with iid mean 0
variance 1 entries scaled by <math>n^{-\gamma -1/2}</math> for <math>\gamma > 0</math>, which
by itself has eigenvalues collapsing to the origin.  What happens to the
eigenvalues when you add a small random noise matrix to the fixed matrix?
There are interesting cases where the eigenvalue distribution is known to
change dramatically when small Gaussian random noise is added, and this talk
will focus on what happens when the noise is <i>not</i> Gaussian.


== Thursday, February 27, [http://mypage.iu.edu/~jthanson/ Jack Hanson], Indiana University Bloomington ==
This is a joint work with Belinschi and Guionnet.


Title: '''Subdiffusive Fluctuations in First-Passage Percolation'''
== March 12, 2020, No seminar ==
''' '''


Abstract: First-passage percolation is a model consisting of a random metric t(x,y) generated by random variables associated to edges of a graph. Many questions and conjectures in this model revolve around the fluctuating properties of this metric on the graph Z^d. In the early 1990s, Kesten showed an upper bound of Cn for the variance of t(0,nx); this was improved to Cn/log(n) by Benjamini-Kalai-Schramm and Benaim-Rossignol for particular choices of distribution. I will discuss recent work (with M. Damron and P. Sosoe) extending this upper bound to general classes of distributions.
== March 19, 2020, Spring break ==
''' '''


== Thursday, March 6, TBA ==
== March 26, 2020, CANCELLED, [https://math.cornell.edu/philippe-sosoe Philippe Sosoe] (Cornell) ==
''' '''


Title: First-passage percolation on Z^d
== April 2, 2020, CANCELLED, [http://pages.cs.wisc.edu/~tl/ Tianyu Liu] (UW Madison)==
''' '''


Abstract:
== April 9, 2020, CANCELLED, [http://stanford.edu/~ajdunl2/ Alexander Dunlap] (Stanford) ==
First-passage percolation is a model consisting of a random metric t(x,y) generated by random variables associated to edges of a graph. Many questions and conjectures in this model revolve around the fluctuating properties of this metric on the graph Z^d. In the early 1990s, Kesten showed an upper bound of Cn for the variance of t(0,nx); this was improved to Cn/log(n) by Benjamini-Kalai-Schramm and Benaim-Rossignol for particular choices of distribution. I will discuss recent work (with M. Damron and P. Sosoe) extending this upper bound to general classes of distributions.
''' '''


== Thursday, March 13, TBA ==
== April 16, 2020, CANCELLED, [https://statistics.wharton.upenn.edu/profile/dingjian/ Jian Ding] (University of Pennsylvania) ==
''' '''


== Thursday, March 20, No Seminar due to Spring Break ==
== April 22-24, 2020, CANCELLED, [http://frg.int-prob.org/ FRG Integrable Probability] meeting ==


== Thursday, March 27, [http://www.stat.wisc.edu/~ane/ Cécile Ané], UW-Madison Department of Statistics ==
3-day event in Van Vleck 911


Title: <b> Application of a birth-death process to model gene gains and losses on a phylogenetic tree </b>
== April 23, 2020, CANCELLED, [http://www.hairer.org/ Martin Hairer] (Imperial College) ==


== Thursday, April 3, TBA ==
[https://www.math.wisc.edu/wiki/index.php/Colloquia Wolfgang Wasow Lecture] at 4pm in Van Vleck 911
 
== April 30, 2020, CANCELLED, [http://willperkins.org/ Will Perkins] (University of Illinois at Chicago) ==
''' '''


== Thursday, April 10, [https://www.math.ucdavis.edu/~romik/home/Dan_Romik_home.html Dan Romik] UC-Davis ==


== Thursday, April 17, TBA ==


== Thursday, April 24, TBA ==


== Thursday, May 1, [http://math.uchicago.edu/~auffing/ Antonio Auffinger] U Chicago ==


== Thursday, May 8, TBA ==






[[Past Seminars]]
[[Past Seminars]]
<!--
== <span style="color:red"> Tuesday, October 22, 4pm, Van Vleck 901</span>, Anton Wakolbinger, Goethe Universität Frankfurt ==
Please note the non-standard time and day, <b><span style="color:red">and the recently revised time and room</span>.</b>
Title: '''The time to fixation of a strongly beneficial mutant in a structured population'''

Latest revision as of 22:18, 12 August 2020


Spring 2020

Thursdays in 901 Van Vleck Hall at 2:30 PM, unless otherwise noted. We usually end for questions at 3:20 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


January 23, 2020, Timo Seppalainen (UW Madison)

Non-existence of bi-infinite geodesics in the exponential corner growth model

Whether bi-infinite geodesics exist has been a significant open problem in first- and last-passage percolation since the mid-80s. A non-existence proof in the case of directed planar last-passage percolation with exponential weights was posted by Basu, Hoffman and Sly in November 2018. Their proof utilizes estimates from integrable probability. This talk describes an independent proof completed 10 months later that relies on couplings, coarse graining, and control of geodesics through planarity and increment-stationary last-passage percolation. Joint work with Marton Balazs and Ofer Busani (Bristol).

January 30, 2020, Scott Smith (UW Madison)

Quasi-linear parabolic equations with singular forcing

The classical solution theory for stochastic ODE's is centered around Ito's stochastic integral. By intertwining ideas from analysis and probability, this approach extends to many PDE's, a canonical example being multiplicative stochastic heat equations driven by space-time white noise. In both the ODE and PDE settings, the solution theory is beyond the scope of classical deterministic theory because of the ambiguity in multiplying a function with a white noise. The theory of rough paths and regularity structures provides a more quantitative understanding of this difficulty, leading to a more refined solution theory which efficiently divides the analytic and probabilistic aspects of the problem, and remarkably, even has an algebraic component.

In this talk, we will discuss a new application of these ideas to stochastic heat equations where the strength of the diffusion is not constant but random, as it depends locally on the solution. These are known as quasi-linear equations. Our main result yields the deterministic side of a solution theory for these PDE's, modulo a suitable renormalization. Along the way, we identify a formally infinite series expansion of the solution which guides our analysis, reveals a nice algebraic structure, and encodes the counter-terms in the PDE. This is joint work with Felix Otto, Jonas Sauer, and Hendrik Weber.

February 6, 2020, Cheuk-Yin Lee (Michigan State)

Sample path properties of stochastic partial differential equations: modulus of continuity and multiple points

In this talk, we will discuss sample path properties of stochastic partial differential equations (SPDEs). We will present a sharp regularity result for the stochastic wave equation driven by an additive Gaussian noise that is white in time and colored in space. We prove the exact modulus of continuity via the property of local nondeterminism. We will also discuss the existence problem for multiple points (or self-intersections) of the sample paths of SPDEs. Our result shows that multiple points do not exist in the critical dimension for a large class of Gaussian random fields including the solution of a linear system of stochastic heat or wave equations.

February 13, 2020, Jelena Diakonikolas (UW Madison)

Langevin Monte Carlo Without Smoothness

Langevin Monte Carlo (LMC) is an iterative algorithm used to generate samples from a distribution that is known only up to a normalizing constant. The nonasymptotic dependence of its mixing time on the dimension and target accuracy is understood mainly in the setting of smooth (gradient-Lipschitz) log-densities, a serious limitation for applications in machine learning. We remove this limitation by providing polynomial-time convergence guarantees for a variant of LMC in the setting of non-smooth log-concave distributions. At a high level, our results follow by leveraging the implicit smoothing of the log-density that comes from a small Gaussian perturbation that we add to the iterates of the algorithm and while controlling the bias and variance that are induced by this perturbation. Based on joint work with Niladri Chatterji, Michael I. Jordan, and Peter L. Bartlett.

February 20, 2020, Philip Matchett Wood (UC Berkeley)

A replacement principle for perturbations of non-normal matrices

There are certain non-normal matrices whose eigenvalues can change dramatically when a small perturbation is added. However, when that perturbation is an iid random matrix, it appears that the eigenvalues become stable after perturbation and only change slightly when further small perturbations are added. Much of the work is this situation has focused on iid random gaussian perturbations. In this talk, we will discuss work on a universality result that allows for consideration of non-gaussian perturbations, and that shows that all perturbations satisfying certain conditions will produce the same limiting eigenvalue measure. Interestingly, this even allows for deterministic perturbations to be considered. Joint work with Sean O'Rourke.

February 27, 2020, No seminar

March 5, 2020, Jiaoyang Huang (IAS)

Large Deviation Principles via Spherical Integrals

In this talk, I'll explain a framework to study the large deviation principle for matrix models and their quantized versions, by tilting the measures using the asymptotics of spherical integrals obtained by Guionnet and Zeitouni. As examples, we obtain

1) the large deviation principle for the empirical distribution of the diagonal entries of $UB_NU^*$, for a sequence of $N\times N$ diagonal matrices $B_N$ and unitary/orthogonal Haar distributed matrices $U$;

2) the large deviation upper bound for the empirical eigenvalue distribution of $A_N+UB_NU^*$, for two sequences of $N\times N$ diagonal matrices $A_N, B_N$, and their complementary lower bounds at "good" probability distributions;

3) the large deviation principle for the Kostka number $K_{\lambda_N \eta_N}$, for two sequences of partitions $\lambda_N, \eta_N$ with at most $N$ rows;

4) the large deviation upper bound for the Littlewood-Richardson coefficients $c_{\lambda_N \eta_N}^{\kappa_N}$, for three sequences of partitions $\lambda_N, \eta_N, \kappa_N$ with at most $N$ rows, and their complementary lower bounds at "good" probability distributions.

This is a joint work with Belinschi and Guionnet.

March 12, 2020, No seminar

March 19, 2020, Spring break

March 26, 2020, CANCELLED, Philippe Sosoe (Cornell)

April 2, 2020, CANCELLED, Tianyu Liu (UW Madison)

April 9, 2020, CANCELLED, Alexander Dunlap (Stanford)

April 16, 2020, CANCELLED, Jian Ding (University of Pennsylvania)

April 22-24, 2020, CANCELLED, FRG Integrable Probability meeting

3-day event in Van Vleck 911

April 23, 2020, CANCELLED, Martin Hairer (Imperial College)

Wolfgang Wasow Lecture at 4pm in Van Vleck 911

April 30, 2020, CANCELLED, Will Perkins (University of Illinois at Chicago)





Past Seminars