## Electronic Communications in Probability

### Inequality of Two Critical Probabilities for Percolation

Jeff Kahn

#### 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.

#### Article information

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

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

https://projecteuclid.org/euclid.ecp/1463608905

Digital Object Identifier
doi:10.1214/ECP.v8-1099

Mathematical Reviews number (MathSciNet)
MR2042758

Zentralblatt MATH identifier
1060.60096

Rights

#### Citation

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

#### References

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