The Annals of Probability
- Ann. Probab.
- Volume 27, Number 3 (1999), 1347-1356.
Critical Percolation on Any Nonamenable Group has no Infinite Clusters
We show that independent percolation on any Cayley graph of a nonamenable group has no infinite components at the critical parameter. This result was obtained by the present authors earlier as a corollary of a general study of group-invariant percolation. The goal here is to present a simpler self-contained proof that easily extends to quasi-transitive graphs with a unimodular automorphism group. The key tool is a “mass-transport” method, which is a technique of averaging in nonamenable settings.
Ann. Probab., Volume 27, Number 3 (1999), 1347-1356.
First available in Project Euclid: 29 May 2002
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Benjamini, Itai; Lyons, Russell; Peres, Yuval; Schramm, Oded. Critical Percolation on Any Nonamenable Group has no Infinite Clusters. Ann. Probab. 27 (1999), no. 3, 1347--1356. doi:10.1214/aop/1022677450. https://projecteuclid.org/euclid.aop/1022677450