We prove an upper bound for the ǫ-mixing time of the symmetric exclusion process on any graph G, with any feasible number of particles. Our estimate is proportional to T RW(G) ln(|V |/ǫ), where |V | is the number of vertices in G and T 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 Erdös-Rényi random graph and Poisson point processes in R d . Our technical tools include a variant of Morris' chameleon process.
Oliveira showed that the mixing time of the exclusion process is in O t R mix · log (|V |) , where t R mix denotes the mixing time of the random walk on G REF .
Mixing of the symmetric exclusion processes in terms of the corresponding single-particle random walk
Annals of Probability 2013, Vol. 41, No. 2, 871-913
Mathematics