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2003 Inequality of Two Critical Probabilities for Percolation
Jeff Kahn
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Electron. Commun. Probab. 8: 184-187 (2003). DOI: 10.1214/ECP.v8-1099

Abstract

We disprove a conjecture of Russ Lyons---that for every locally finite, connected graph $G$, the critical probability for (Bernoulli bond) percolation on $G$ is equal to the "first moment method" lower bound on this probability---and propose a possible alternative.

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Jeff Kahn. "Inequality of Two Critical Probabilities for Percolation." Electron. Commun. Probab. 8 184 - 187, 2003. https://doi.org/10.1214/ECP.v8-1099

Information

Accepted: 27 December 2003; Published: 2003
First available in Project Euclid: 18 May 2016

zbMATH: 1060.60096
MathSciNet: MR2042758
Digital Object Identifier: 10.1214/ECP.v8-1099

Subjects:
Primary: 60C05, 82B43

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