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

TL;DR

This paper establishes an upper bound on the mixing time of symmetric exclusion processes based on the mixing time of the associated single-particle random walk, with implications for various graph structures.

Contribution

It provides a new upper bound for the mixing time of symmetric exclusion processes in terms of single-particle random walk mixing times, applicable to diverse graph types.

Findings

Upper bound proportional to T_RW(G) * log(|V|/ε) for mixing time

New results for expanders, percolation clusters, and Erdős-Rényi graphs

Application of a variant of Morris's chameleon process

Abstract

We prove an upper bound for the $\varepsilon$-mixing time of the symmetric exclusion process on any graph G, with any feasible number of particles. Our estimate is proportional to $\mathsf{T}_{\mathsf{RW}(G)}\ln(|V|/\varepsilon)$, 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.