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Is the critical percolation probability local?
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  • Published: 19 November 2009

Is the critical percolation probability local?

  • Itai Benjamini1,
  • Asaf Nachmias2 &
  • Yuval Peres2 

Probability Theory and Related Fields volume 149, pages 261–269 (2011)Cite this article

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  • 30 Citations

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Abstract

We show that the critical probability for percolation on a d-regular non-amenable graph of large girth is close to the critical probability for percolation on an infinite d-regular tree. We also prove a finite analogue of this statement, valid for expander graphs, without any girth assumption.

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Author information

Authors and Affiliations

  1. The Weizmann Institute of Science, POB 76100, Rehovot, Israel

    Itai Benjamini

  2. Microsoft Research, One Microsoft way, Redmond, WA, 98052-6399, USA

    Asaf Nachmias & Yuval Peres

Authors
  1. Itai Benjamini
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  2. Asaf Nachmias
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  3. Yuval Peres
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Corresponding author

Correspondence to Itai Benjamini.

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Cite this article

Benjamini, I., Nachmias, A. & Peres, Y. Is the critical percolation probability local?. Probab. Theory Relat. Fields 149, 261–269 (2011). https://doi.org/10.1007/s00440-009-0251-5

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  • Received: 14 March 2009

  • Revised: 13 May 2009

  • Published: 19 November 2009

  • Issue Date: February 2011

  • DOI: https://doi.org/10.1007/s00440-009-0251-5

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Mathematics Subject Classification (2000)

  • 60K35
  • 82B43
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