Past Probability Seminars Spring 2020
Thursdays in 901 Van Vleck Hall at 2:25 PM, unless otherwise noted. We usually end for questions at 3:15 PM.
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Thursday, September 14, 2017, Brian Rider Temple University
A universality result for the random matrix hard edge
The hard edge refers to the distribution of the smallest singular value for certain ensembles of random matrices, or, and what is the same, that of the minimal point of a logarithmic gas constrained to the positive half line. For any "inverse temperature" and “quadratic" potential the possible limit laws (as the dimension, or number of particles, tends to infinity) was characterized by Jose Ramirez and myself in terms of the spectrum of a (random) diffusion generator. Here we show this picture persists for more general convex polynomial potentials. Joint work with Patrick Waters.
Thursday, October 19, 2017 Varun Jog, UW-Madison ECE and Grainger Institute
Title: Teaching and learning in uncertainty
Abstract: We investigate a simple model for social learning with two characters: a teacher and a student. The teacher's goal is to teach the student the state of the world [math]\Theta[/math], however, the teacher herself is not certain about [math]\Theta[/math] and needs to simultaneously learn it and teach it. We examine several natural strategies the teacher may employ to make the student learn as fast as possible. Our primary technical contribution is analyzing the exact learning rates for these strategies by studying the large deviation properties of the sign of a transient random walk on [math]\mathbb Z[/math].
Thursday, October 26, 2017, Konstantin Matetski Toronto
Title: The KPZ fixed point
Abstract: The KPZ fixed point is the Markov process at the centre of the KPZ universality class. In the talk we describe the exact solution of the totally asymmetric simple exclusion process, which is one of the models in the KPZ universality class, and provide a description of the KPZ fixed point in the 1:2:3 scaling limit. This is a joint work with Jeremy Quastel and Daniel Remenik.
Thursday, November 9, 2017, Chen Jia, University of Texas at Dallas
Mathematical foundation of nonequilibrium fluctuation-dissipation theorems and a biological application
The fluctuation-dissipation theorem (FDT) for equilibrium states is one of the classical results in equilibrium statistical physics. In recent years, many efforts have been devoted to generalizing the classical FDT to systems far from equilibrium. This was considered as one of the most significant progress of nonequilibrium statistical physics over the past two decades. In this talk, I will introduce our recent work on the rigorous mathematical foundation of the nonequilibrium FDTs for inhomogeneous diffusion processes and inhomogeneous continuous-time Markov chains. I will also talk about the application of the nonequilibrium FDTs to a practical biological problem called sensory adaptation.