On the mixing time of simple random walk on the super critical   percolation cluster
  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. 
Itai Benjamini and Elchanan Mossel