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

Itai Benjamini; Elchanan Mossel

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

Probability 2007-05-23 v3 Combinatorics

Authors: Itai Benjamini , Elchanan Mossel

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 $d \geq 2$ 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.

Keywords

mixing time simple random walk percolation cluster supercritical percolation robustness

Cite

@article{arxiv.math/0011092,
  title  = {On the mixing time of simple random walk on the super critical percolation cluster},
  author = {Itai Benjamini and Elchanan Mossel},
  journal= {arXiv preprint arXiv:math/0011092},
  year   = {2007}
}

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