On the mixing time of a simple random walk on the super critical percolation cluster

Abstract

We study the robustness under perturbations of mixing times, by studying mixing times of random walks in percolation clusters inside boxes in Z d . We show that for d≥2 and p>p c (Z d ), the mixing time of simple random walk on the largest cluster inside is Θ(n 2 ) – thus the mixing time is robust up to a constant factor. The mixing time bound utilizes the Lovasz-Kannan average conductance method. This is the first non-trivial application of this method which yields a tight result.