Journal
PROBABILITY THEORY AND RELATED FIELDS
Volume 125, Issue 3, Pages 408-420Publisher
SPRINGER-VERLAG
DOI: 10.1007/s00440-002-0246-y
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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 greater than or equal to 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 a constant factor. The mixing time bound utilizes the Lovasz-Kannan average conductance method. This is the first non-trivial application of this method which yields a tight result.
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