Electronic Communications in Probability

Electronic Communications in Probability > Vol. 8 (2003) > Paper 21

Inequality of Two Critical Probabilities for Percolation

Jeff Kahn, Rutgers University, USA

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.

Full text: PDF

Pages: 184-187

Published on: December 27, 2003

Bibliography

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Electronic Communications in Probability. ISSN: 1083-589X