Difference between revisions of "Probability Seminar"

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(March 7, TBA)
(March 7, Shamgar Gurevitch UW-Madison)
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== March 7, [https://www.math.wisc.edu/~shamgar/ Shamgar Gurevitch] [https://www.math.wisc.edu/ UW-Madison]==
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== March 7, TBA ==
 
 
Title: '''Harmonic Analysis on GLn over finite fields, and Random Walks'''
 
 
 
Abstract: There are many formulas that express interesting properties of a group G in terms of sums over its characters. For evaluating or estimating these sums, one of the most salient quantities to understand is the {\it character ratio}:
 
 
 
$$
 
trace(\rho(g))/dim(\rho),
 
$$
 
 
 
for an irreducible representation $\rho$ of G and an element g of G. For example, Diaconis and Shahshahani stated a formula of this type for analyzing G-biinvariant random walks on G. It turns out that, for classical groups G over finite fields (which provide most examples of finite simple groups), there is a natural invariant of representations that provides strong information on the character ratio. We call this invariant {\it rank}. This talk will discuss the notion of rank for GLn over finite fields, and apply the results to random walks. This is joint work with Roger Howe (Yale and Texas AM).
 
  
 
== March 14, TBA ==
 
== March 14, TBA ==

Revision as of 20:53, 4 February 2019


Spring 2019

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


January 31, Oanh Nguyen, Princeton

Title: Survival and extinction of epidemics on random graphs with general degrees

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 $\lambda>0$. Joint work with Shankar Bhamidi, Danny Nam, and Allan Sly.

Wednesday, February 6 at 4:00pm in Van Vleck 901 , Li-Cheng Tsai, Columbia University

Title: When particle systems meet PDEs

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..

February 7, Yu Gu, CMU

Title: Fluctuations of the KPZ equation in d\geq 2 in a weak disorder regime

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.

February 14, TBA

February 21, TBA

Wednesday, February 27 at 1:10pm Jon Peterson, Purdue

  Please note the unusual day and time.  

March 7, TBA

March 14, TBA

March 21, Spring Break, No seminar

March 28, TBA

April 4, TBA

April 11, Eviatar Proccia, Texas A&M

April 18, Andrea Agazzi, Duke

April 25, Kavita Ramanan, Brown

April 26, Colloquium, Kavita Ramanan, Brown

April 26, TBA

May 2, TBA

Past Seminars