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On the mixing time of a simple random walk on the super critical percolation cluster
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  • Published: March 2003

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

  • Itai Benjamini1 &
  • Elchanan Mossel2 

Probability Theory and Related Fields volume 125, pages 408–420 (2003)Cite this article

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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Authors and Affiliations

  1. The Weizmann Institute of Science, The Faculty of Mathematics and Computer Science, POB 26, Rehovot, 76100 ISRAEL. e-mail: itai@wisdom.weizmann.ac.il, , , , , , IL

    Itai Benjamini

  2. Computer Science division 384 Soda Hall, University of California, Berkeley, CA 94720-1776, USA. e-mail: mossel@microsoft.com, , , , , , US

    Elchanan Mossel

Authors
  1. Itai Benjamini
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  2. Elchanan Mossel
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Additional information

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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  • Issue Date: March 2003

  • DOI: https://doi.org/10.1007/s00440-002-0246-y

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Keywords

  • Random Walk
  • Large Cluster
  • Constant Factor
  • Percolation Cluster
  • Average Conductance
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