Difference between revisions of "Probability Seminar"

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__NOTOC__
 
__NOTOC__
  
= Spring 2019 =
+
= Fall 2019 =
  
<b>Thursdays in 901 Van Vleck Hall at 2:25 PM</b>, unless otherwise noted.  
+
<b>Thursdays in 901 Van Vleck Hall at 2:30 PM</b>, unless otherwise noted.  
<b>We  usually end for questions at 3:15 PM.</b>
+
<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  
 
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]
 
[mailto:join-probsem@lists.wisc.edu join-probsem@lists.wisc.edu]
  
 +
 +
== September 12, 2019, [https://perso.univ-rennes1.fr/victor.kleptsyn/ Victor Kleptsyn], CNRS and University of Rennes 1 ==
 +
'''Furstenberg theorem: now with a parameter!'''
  
 +
The classical Furstenberg theorem describes the (almost sure) behaviour of a random product of independent matrices; their norms turn out to grow exponentially. In our joint work with A. Gorodetski, we study what happens if the random matrices depend on an additional parameter.
 +
It turns out that in this new situation, the conclusion changes. Namely, under some conditions, there almost surely exists a (random) "exceptional" set on parameters where the lower limit for the Lyapunov exponent vanishes.
 +
Our results are related to the Anderson localization in dimension one, providing a purely dynamical viewpoint on its proof. I will also speak about some generalizations and related open questions.
  
== January 31, [https://www.math.princeton.edu/people/oanh-nguyen Oanh Nguyen], [https://www.math.princeton.edu/ Princeton] ==
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== September 19, 2019, [http://math.columbia.edu/~xuanw  Xuan Wu], Columbia University==
  
Title: '''Survival and extinction of epidemics on random graphs with general degrees'''
+
'''A Gibbs resampling method for discrete log-gamma line ensemble.'''
  
Abstract: We establish the necessary and sufficient criterion for the contact process on Galton-Watson trees (resp. random graphs) to exhibit the phase of extinction (resp. short survival). We prove that the survival threshold $\lambda_1$ for a Galton-Watson tree is strictly positive if and only if its offspring distribution has an exponential tail, settling a conjecture by Huang and Durrett. On the random graph with degree distribution $D$, we show that if $D$ has an exponential tail, then for small enough $\lambda$ the contact process with the all-infected initial condition survives for polynomial time with high probability, while for large enough $\lambda$ it runs over exponential time with high probability. When $D$ is subexponential, the contact process typically displays long survival for any fixed $\lambda>0$.
+
In this talk we will construct the discrete log-gamma line ensemble, which is assocaited with inverse gamma polymer model. This log-gamma line ensemble enjoys a random walk Gibbs resampling invariance that follows from the integrable nature of the inverse gamma polymer model via geometric RSK correspondance. By exploiting such resampling invariance, we show the tightness of this log-gamma line ensemble under weak noise scaling. Furthermore, a Gibbs property, as enjoyed by KPZ line ensemble, holds for all subsequential limits.
Joint work with Shankar Bhamidi, Danny Nam, and Allan Sly.
 
  
== February 6, [https://lc-tsai.github.io/ Li-Cheng Tsai], [https://lc-tsai.github.io/ Columbia University] ==
+
== October 3, 2019, TBA ==
  
Title: '''When particle systems meet PDEs'''
+
== October 10, 2019, NO SEMINAR - [https://sites.math.northwestern.edu/mwp/ Midwest Probability Colloquium] ==
  
Abstract: Interacting particle systems are models that involve many randomly evolving agents (i.e., particles). These systems are widely used in describing real-world phenomena. In this talk we will walk through three facets of interacting particle systems, namely the law of large numbers, random fluctuations, and large deviations. Within each facet, I will explain how Partial Differential Equations (PDEs) play a role in understanding the systems..
+
== October 17, 2019, [https://www.usna.edu/Users/math/hottovy/index.php Scott Hottovy], USNA ==
  
== February 7, [http://www.math.cmu.edu/~yug2/ Yu Gu], [https://www.cmu.edu/math/index.html CMU] ==
+
== October 24, 2019, [https://math.temple.edu/~brider/ Brian Rider], Temple University ==
  
Title: '''Fluctuations of the KPZ equation in d\geq 2 in a weak disorder regime'''
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== October 31, 2019, [http://math.mit.edu/~elmos/ Elchanan Mossel], MIT ==
  
Abstract: We will discuss some recent work on the Edwards-Wilkinson limit of the KPZ equation with a small coupling constant in d\geq 2.
+
== November 7, 2019, [https://people.kth.se/~tobergg/ Tomas Berggren], KTH Stockholm ==
  
== February 14, TBA ==
+
== November 14, 2019, [https://math.mit.edu/directory/profile.php?pid=2076 Benjamin Landon], MIT ==
== February 21, TBA ==
 
==  <span style="color:red"> Wednesday, February 27 at 1:10pm</span> [http://www.math.purdue.edu/~peterson/ Jon Peterson], [http://www.math.purdue.edu/ Purdue] ==
 
  
 +
== November 21, 2019, TBA ==
  
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== November 28, 2019, Thanksgiving (no seminar) ==
<b><span style="color:red">&emsp; Please note the unusual day and time.
 
&emsp; </span></b>
 
</div>
 
  
== March 7, TBA ==
+
== December 5, 2019, Vadim Gorin, UW Madison ==
== March 14, TBA ==
 
== March 21, Spring Break, No seminar ==
 
  
== March 28, TBA ==
 
== April 4, TBA ==
 
== April 11, [https://sites.google.com/site/ebprocaccia/ Eviatar Proccia], [http://www.math.tamu.edu/index.html Texas A&M] ==
 
 
== April 18, [https://services.math.duke.edu/~agazzi/index.html Andrea Agazzi], [https://math.duke.edu/ Duke] ==
 
 
== April 25, [https://www.brown.edu/academics/applied-mathematics/kavita-ramanan Kavita Ramanan], [https://www.brown.edu/academics/applied-mathematics/ Brown] ==
 
 
== April 26, Colloquium, [https://www.brown.edu/academics/applied-mathematics/kavita-ramanan Kavita Ramanan], [https://www.brown.edu/academics/applied-mathematics/ Brown] ==
 
 
== April 26, TBA ==
 
== May 2, TBA ==
 
  
  
 
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==<span style="color:red"> Friday, August 10, 10am, B239 Van Vleck </span> András Mészáros, Central European University, Budapest ==
 
  
 +
== <span style="color:red"> Wednesday, February 6 at 4:00pm in Van Vleck 911</span> , [https://lc-tsai.github.io/ Li-Cheng Tsai], [https://www.columbia.edu/ Columbia University] ==
  
Title: '''The distribution of sandpile groups of random regular graphs'''
+
Title: '''When particle systems meet PDEs'''
  
Abstract:
+
Abstract: Interacting particle systems are models that involve many randomly evolving agents (i.e., particles). These systems are widely used in describing real-world phenomena. In this talk we will walk through three facets of interacting particle systems, namely the law of large numbers, random fluctuations, and large deviations. Within each facet, I will explain how Partial Differential Equations (PDEs) play a role in understanding the systems..
We study the distribution of the sandpile group of random <math>d</math>-regular graphs. For the directed model we prove that it follows the Cohen-Lenstra heuristics, that is, the probability that the <math>p</math>-Sylow subgroup of the sandpile group is a given <math>p</math>-group <math>P</math>, is proportional to <math>|\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>d</math>-regular directed graphs are invertible with high probability to the undirected case.
 
  
 +
== <span style="color:red">'''Tuesday''' </span>, May 7,  Van Vleck 901, 2:25pm, Duncan Dauvergne (Toronto) ==
  
==September 20, [http://math.columbia.edu/~hshen/ Hao Shen], [https://www.math.wisc.edu/ UW-Madison] ==
 
  
Title: '''Stochastic quantization of Yang-Mills'''
+
<div style="width:250px;height:50px;border:5px solid black">
 
+
<b><span style="color:red">&emsp; Please note the unusual day.
Abstract:
+
&emsp; </span></b>
"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.
+
</div>
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].
+
Title: '''The directed landscape'''
  
 +
Abstract: I will describe the construction of the full scaling limit of (Brownian) last passage percolation: the directed landscape. The directed landscape can be thought of as a random scale-invariant `directed' metric on the plane, and last passage paths converge to directed geodesics in this metric. The directed landscape is expected to be a universal scaling limit for general last passage and random growth models (i.e. TASEP, the KPZ equation, the longest increasing subsequence in a random permutation). Joint work with Janosch Ormann and Balint Virag.
 
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Latest revision as of 13:05, 20 September 2019


Fall 2019

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


September 12, 2019, Victor Kleptsyn, CNRS and University of Rennes 1

Furstenberg theorem: now with a parameter!

The classical Furstenberg theorem describes the (almost sure) behaviour of a random product of independent matrices; their norms turn out to grow exponentially. In our joint work with A. Gorodetski, we study what happens if the random matrices depend on an additional parameter. It turns out that in this new situation, the conclusion changes. Namely, under some conditions, there almost surely exists a (random) "exceptional" set on parameters where the lower limit for the Lyapunov exponent vanishes. Our results are related to the Anderson localization in dimension one, providing a purely dynamical viewpoint on its proof. I will also speak about some generalizations and related open questions.

September 19, 2019, Xuan Wu, Columbia University

A Gibbs resampling method for discrete log-gamma line ensemble.

In this talk we will construct the discrete log-gamma line ensemble, which is assocaited with inverse gamma polymer model. This log-gamma line ensemble enjoys a random walk Gibbs resampling invariance that follows from the integrable nature of the inverse gamma polymer model via geometric RSK correspondance. By exploiting such resampling invariance, we show the tightness of this log-gamma line ensemble under weak noise scaling. Furthermore, a Gibbs property, as enjoyed by KPZ line ensemble, holds for all subsequential limits.

October 3, 2019, TBA

October 10, 2019, NO SEMINAR - Midwest Probability Colloquium

October 17, 2019, Scott Hottovy, USNA

October 24, 2019, Brian Rider, Temple University

October 31, 2019, Elchanan Mossel, MIT

November 7, 2019, Tomas Berggren, KTH Stockholm

November 14, 2019, Benjamin Landon, MIT

November 21, 2019, TBA

November 28, 2019, Thanksgiving (no seminar)

December 5, 2019, Vadim Gorin, UW Madison

Past Seminars