Probability Seminar: Difference between revisions

From UW-Math Wiki
Jump to navigation Jump to search
VisualWikitext
(47 intermediate revisions by 4 users not shown)
Line 2: Line 2:
[[Probability | Back to Probability Group]]
[[Probability | Back to Probability Group]]


= Fall 2022 =
[[Past Seminars]]


<b>Thursdays at 2:30 PM either in 901 Van Vleck Hall or on Zoom</b>  
= Fall 2023 =
<b>Thursdays at 2:30 PM either in 901 Van Vleck Hall or on Zoom</b>


We usually end for questions at 3:20 PM.
We usually end for questions at 3:20 PM.


[https://uwmadison.zoom.us/j/91828707031?pwd=YUJXMUJkMDlPR0VRdkRCQVJtVndIdz09 ZOOM LINK. Valid only for online seminars.]
== September 14, 2023: [https://www.mathjunge.com/ Matthew Junge] (CUNY) ==
 
'''The frog model on trees'''
If you would like to sign up for the email list to receive seminar announcements then please join [https://groups.google.com/a/g-groups.wisc.edu/forum/#!forum/probsem our group].
 
 
== September 22, 2022, in person: [https://sites.google.com/site/pierreyvesgl/home Pierre Yves Gaudreau Lamarre] (University of Chicago)   ==
 
'''Moments of the Parabolic Anderson Model with Asymptotically Singular Noise'''
The Parabolic Anderson Model (PAM) is a stochastic partial differential equation that describes the time-evolution of particle system with the following dynamics: Each particle in the system undergoes a diffusion in space, and as they are moving through space, the particles can either multiply or get killed at a rate that depends on a random environment.
One of the fundamental problems in the theory of the PAM is to understand its behavior at large times. More specifically, the solution of the PAM at large times tends to be intermittent, meaning that most of the particles concentrate in small regions where the environment is most favorable for particle multiplication.
In this talk, we discuss a new technique to study intermittency in the PAM with a singular random environment. In short, the technique consists of approximating the singular PAM with a regularized version that becomes increasingly singular as time goes to infinity.
This talk is based on a joint work with Promit Ghosal and Yuchen Liao.
 
== September 29, 2022, in person: Christian Gorski (Northwestern University)    ==


The frog model describes random activation and spread. Think combustion or an epidemic. I have studied these dynamics on ''d''-ary trees for ten years. I will discuss our progress and what remains to be done.


== October 6, 2022, in person: [https://danielslonim.github.io/ Daniel Slonim] (University of Virginia)   ==  
== September 21, 2023: [https://yierlin.me/ Yier Lin] (U. Chicago) ==
'''Large Deviations of the KPZ Equation and Most Probable Shapes'''


'''Random Walks in (Dirichlet) Random Environments with Jumps on Z'''


We introduce the model of random walks in random environments (RWRE), which are random Markov chains on the integer lattice. These random walks are well understood in the nearest-neighbor, one-dimensional case due to reversibility of almost every Markov chain. For example, directional transience and limiting speed can be characterized in terms of simple expectations involving the transition probabilities at a single site. The reversibility is lost, however, if we go up to higher dimensions or relax the nearest-neighbor assumption by allowing jumps, and therefore much less is known in these models. Despite this non-reversibility, certain special cases have proven to be more tractable. Random Walks in Dirichlet environments (RWDE), where the transition probability vectors are drawn according to a Dirichlet distribution, have been fruitfully studied in the nearest-neighbor, higher dimensional setting. We look at RWDE in one dimension with jumps and characterize when the walk is ballistic: that is, when it has non-zero limiting velocity. It turns out that in this model, there are two factors which can cause a directionally transient walk to have zero limiting speed: finite trapping and large-scale backtracking. Finite trapping involves finite subsets of the graph where the walk is liable to get trapped for a long time. It is a highly local phenomenon that depends heavily on the structure of the underlying graph. Large-scale backtracking is a more global and one-dimensional phenomenon. The two operate "independently" in the sense that either can occur with or without the other. Moreover, if neither factor on its own is enough to cause zero speed, then the walk is ballistic, so the two factors cannot conspire together to slow a walk down to zero speed if neither is sufficient to do so on its own. This appearance of two independent factors affecting ballisticity is a new feature not seen in any previously studied RWRE models.  
The KPZ equation is a stochastic PDE that plays a central role in a class of random growth phenomena. In this talk, we will explore the Freidlin-Wentzell LDP for the KPZ equation through the lens of the variational principle. Additionally, we will explain how to extract various limits of the most probable shape of the KPZ equation using the variational formula. We will also discuss an alternative approach for studying these quantities using the method of moments. This talk is based in part on joint works with Pierre Yves Gaudreau Lamarre and Li-Cheng Tsai.


== October 13, 2022, [https://uwmadison.zoom.us/j/91828707031?pwd=YUJXMUJkMDlPR0VRdkRCQVJtVndIdz09 ZOOM]: [https://www.maths.univ-evry.fr/pages_perso/loukianova/ Dasha Loukianova] (Université d'Évry Val d'Essonne)   ==  
== September 28, 2023: [https://warwick.ac.uk/fac/sci/statistics/staff/academic-research/rosati/ Tommaso Rosati] (U. Warwick) ==
'''The Allen-Cahn equation with weakly critical initial datum'''


We study the 2D Allen-Cahn with white noise initial datum. In a weak coupling regime, where the nonlinearity is damped in relation to the smoothing of the initial condition, we prove Gaussian fluctuations. The effective variance that appears can be described as the solution to an ODE. Our proof builds on a Wild expansion of the solution, which is controlled through precise combinatorial estimates. Joint work with Simon Gabriel and Nikolaos Zygouras.


== October 27, 2022, [https://uwmadison.zoom.us/j/91828707031?pwd=YUJXMUJkMDlPR0VRdkRCQVJtVndIdz09 ZOOM]: [https://www-users.cse.umn.edu/~arnab/ Arnab Sen] (University of Minnesota, Twin Cities) ==
== October 5, 2023: ==
'''Abstract, title: TBA'''


== October 12, 2023: No Seminar ==


== November 3, 2022, in person: [https://www.ias.edu/scholars/sky-yang-cao Sky Cao] (Institute for Advanced Study)  ==  
== October 19, 2023: ==


== October  26, 2023: Yuchen Liao (UW - Madison) ==
'''Abstract, title: TBA'''


== November 10, 2022, in person: TBD  ==  
== November 2, 2023: [http://homepages.math.uic.edu/~couyang/ Cheng Ouyang] (U. Illinois Chicago) ==
'''Abstract, title: TBA'''


== November 9, 2023: [https://scottandrewsmith.github.io/ Scott Smith] (Chinese Academy of Sciences) ==
'''Abstract, title: TBA'''


== November 17, 2022, [https://uwmadison.zoom.us/j/91828707031?pwd=YUJXMUJkMDlPR0VRdkRCQVJtVndIdz09 ZOOM]: [https://sites.google.com/site/leandroprpimentel/ Leandro Pimentel] (Federal University of Rio de Janeiro)  ==
== November 16, 2023: ==
'''Abstract, title: TBA'''


== November 23, 2023: No Seminar ==
'''No seminar. Thanksgiving.'''


== December 1, in person: [https://cims.nyu.edu/~ajd594/ Alex Dunlap] (Courant Institute)   ==  
== November 30, 2023: [http://web.mit.edu/youngtak/www/homepage.html Youngtak Sohn] (MIT) ==
'''Abstract, title: TBA'''


 
== December 7, 2023: Minjae Park (U. Chicago) ==
== December 8, 2022, in person: [https://sites.northwestern.edu/juliagaudio/ Julia Gaudio] (Northwestern University)   ==  
'''Abstract, title: TBA'''
 
 
[[Past Seminars]]

Revision as of 13:28, 25 September 2023

Back to Probability Group

Past Seminars

Fall 2023

Thursdays at 2:30 PM either in 901 Van Vleck Hall or on Zoom

We usually end for questions at 3:20 PM.

September 14, 2023: Matthew Junge (CUNY)

The frog model on trees

The frog model describes random activation and spread. Think combustion or an epidemic. I have studied these dynamics on d-ary trees for ten years. I will discuss our progress and what remains to be done.

September 21, 2023: Yier Lin (U. Chicago)

Large Deviations of the KPZ Equation and Most Probable Shapes


The KPZ equation is a stochastic PDE that plays a central role in a class of random growth phenomena. In this talk, we will explore the Freidlin-Wentzell LDP for the KPZ equation through the lens of the variational principle. Additionally, we will explain how to extract various limits of the most probable shape of the KPZ equation using the variational formula. We will also discuss an alternative approach for studying these quantities using the method of moments. This talk is based in part on joint works with Pierre Yves Gaudreau Lamarre and Li-Cheng Tsai.

September 28, 2023: Tommaso Rosati (U. Warwick)

The Allen-Cahn equation with weakly critical initial datum

We study the 2D Allen-Cahn with white noise initial datum. In a weak coupling regime, where the nonlinearity is damped in relation to the smoothing of the initial condition, we prove Gaussian fluctuations. The effective variance that appears can be described as the solution to an ODE. Our proof builds on a Wild expansion of the solution, which is controlled through precise combinatorial estimates. Joint work with Simon Gabriel and Nikolaos Zygouras.

October 5, 2023:

Abstract, title: TBA

October 12, 2023: No Seminar

October 19, 2023:

October 26, 2023: Yuchen Liao (UW - Madison)

Abstract, title: TBA

November 2, 2023: Cheng Ouyang (U. Illinois Chicago)

Abstract, title: TBA

November 9, 2023: Scott Smith (Chinese Academy of Sciences)

Abstract, title: TBA

November 16, 2023:

Abstract, title: TBA

November 23, 2023: No Seminar

No seminar. Thanksgiving.

November 30, 2023: Youngtak Sohn (MIT)

Abstract, title: TBA

December 7, 2023: Minjae Park (U. Chicago)

Abstract, title: TBA

Retrieved from "https://wiki.math.wisc.edu/index.php?title=Probability_Seminar&oldid=25312"