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≥2 and p>p c (Z d), the mixing time of simple random walk on the largest cluster inside is Θ(n 2) – thus the mixing time is robust up to a constant factor. The mixing time bound utilizes the Lovàsz-Kannan average conductance method. This is the first non-trivial application of this method which yields a tight result.
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Received: 16 December 2001 / Revised version: 13 August 2002 / Published online: 19 December 2002
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Benjamini, I., Mossel, E. On the mixing time of a simple random walk on the super critical percolation cluster. Probab Theory Relat Fields 125, 408–420 (2003). https://doi.org/10.1007/s00440-002-0246-y
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DOI: https://doi.org/10.1007/s00440-002-0246-y