Mixing of the symmetric exclusion processes in terms of the corresponding single-particle random walk

Abstract

We prove an upper bound for the $\epsilon$-mixing time of the symmetric exclusion process on any graph G, with any feasible number of particles. Our estimate is proportional to ${\mathsf{T}}_{\mathsf{RW}(G)}\ln (|V|/\epsilon )$, where |V| is the number of vertices in G, and ${\mathsf{T}}_{\mathsf{RW}(G)}$ is the 1/4-mixing time of the corresponding single-particle random walk. This bound implies new results for symmetric exclusion on expanders, percolation clusters, the giant component of the Erdos-Renyi random graph and Poisson point processes in ${\mathbb{R}}^d$. Our technical tools include a variant of Morris's chameleon process.

Published in at http://dx.doi.org/10.1214/11-AOP714 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

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