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

Itai Benjamini, Elchanan Mossel

Published 2000-11-14, updated 2002-02-26Version 3

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 $d \geq 2$ and $p > p_c(\Z^d)$, the mixing time of simple random walk on the largest cluster inside $\{-n,...,n\}^d$ is $\Theta(n^2)$ - thus the mixing time is robust up to constant factor.