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

We prove an upper bound for the e-mixing time of the symmetric exclusion process on any graph G, with any feasible number of particles. Our estimate is proportional to TRW(G)ln(|V|/e), where |V| is the number of vertices in G, and TRW(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 Rd. Our technical tools include a variant of Morris’s chameleon process.

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