Invited Speaker - Roberto Imbuzeiro Oliveira (IMPA)

Title:

The symmetric exclusion process on not-too-irregular graphs.

Abstract:

The k-particle symmetric exclusion process on a graph G is a stochastic process where k particles occupy distinct vertices of G and perform independent random walks, except that jumps to occupied sites are supressed. It is a prototypical example of a Markov chain built from simpler processes that interact, and it is very well-studied in the interacting particle systems literature. However, its mixing properties are not very well understood outside of a few special cases such as G=(Z/nZ)^d. We will show that the eps-mixing time of symmetric exclusion on any finite graph is bounded by C r T_{RW} ln(|V(G)|/eps), where C>0 is a universal constant, T_{RW} is the 1/e-mixing time of simple random walk on G and r is a "irregularity parameter" that is at most the ratio of maximal to average degree. Our bound is of the optimal order in many special cases, including certain "disordered" graphs built from random point processes or supercritical percolation clusters. Our main tools are an extension of the techniques of Morris for (Z/nZ)^d (the so-called chamaleon process) and tight bounds for the case of two particles, which we derive via coupling and the negative correlation property of the exclusion process.