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

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

2000-11-14

arxiv.org/abs/math/0011092v3

Mathematics

Probability

Scientific paper

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.

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