Share on Facebook Tweet on Twitter Share on LinkedIn Share by email
Mixing-Time and Cut-Off Window for the Exclusion Process on 1-Dimensional Graphs

Speaker  Hubert Lacoin

Affiliation  Université Paris Dauphine

Host  Yuval Peres

Duration  01:13:02

Date recorded  25 February 2014

We consider the exclusion process with k particle on the circle or segment of lenght N (with k≤ N/2). This is a Markov chain that can be described as follows: k (unlabeled) particles are moving on a graph with the rule that each site can be occupied only by one particle, each particle jump with rate one on each of the neighboring sites, but the jumps are cancelled when a particle tries to jump on a site which is already occupied. The equilibrium state for this dynamics is the uniform measure over all possible particle configuration, and in our talk we want to investigate how much time the system needs to reach equilibrium in terms of total variation distance. We give a sharp answer for both the segment and the circle and discuss the connection with the adjacent transposition shuffle.

©2014 Microsoft Corporation. All rights reserved.
> Mixing-Time and Cut-Off Window for the Exclusion Process on 1-Dimensional Graphs