Random walks on the Symmetric Group and Representation Theory

Random walks on the Symmetric Group and Representation Theory
June, 12, 2018
11:30
Room 861 Electrical Eng. Building Technion City

Probability and Stochastic Processes Seminar

Speaker: Doron Puder

Affiliation: TAU

Aldous’ Spectral gap conjecture, proved in 2009 by Caputo, Liggett and Richthammer, states the following a priori very surprising fact: the spectral gap of a random walk on a finite graph is equal to the spectral gap of the interchange process on the same graph. This seminal result has a very natural interpretation in Representation Theory, which leads to natural conjectural generalizations. In joint work with Ori Parzanchevski, we study some of these possible generalizations, clarify the picture in the case of normal generating sets and reach a more refined conjecture. No prior knowledge on any of the topics will be assumed.