Electronic Communications in Probability

Inequality of Two Critical Probabilities for Percolation

Jeff Kahn

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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.

Article information

Electron. Commun. Probab., Volume 8 (2003), paper no. 21, 184-187.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60C05: Combinatorial probability 82B43: Percolation [See also 60K35]

This work is licensed under aCreative Commons Attribution 3.0 License.


Kahn, Jeff. Inequality of Two Critical Probabilities for Percolation. Electron. Commun. Probab. 8 (2003), paper no. 21, 184--187. doi:10.1214/ECP.v8-1099. https://projecteuclid.org/euclid.ecp/1463608905

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