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

Original · EN

We study the robustness under perturbations of mixing times, by studying mixing times of random walks in percolation clusters inside boxes in ᵈ. We show that for d ≥ 2 and p > pc(ᵈ), the mixing time of simple random walk on the largest cluster inside {-n,...,n}ᵈ is Θ(n²) - thus the mixing time is robust up to constant factor.