Open Access
November 2006 Neighboring clusters in Bernoulli percolation
Adám Timár
Ann. Probab. 34(6): 2332-2343 (November 2006). DOI: 10.1214/009117906000000485


We consider Bernoulli percolation on a locally finite quasi-transitive unimodular graph and prove that two infinite clusters cannot have infinitely many pairs of vertices at distance 1 from one another or, in other words, that such graphs exhibit “cluster repulsion.” This partially answers a question of Häggström, Peres and Schonmann.


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Adám Timár. "Neighboring clusters in Bernoulli percolation." Ann. Probab. 34 (6) 2332 - 2343, November 2006.


Published: November 2006
First available in Project Euclid: 13 February 2007

zbMATH: 1112.60085
MathSciNet: MR2294984
Digital Object Identifier: 10.1214/009117906000000485

Primary: 60K35 , 82B43
Secondary: 60B99

Keywords: Cluster repulsion , nonamenable , percolation , touching clusters

Rights: Copyright © 2006 Institute of Mathematical Statistics

Vol.34 • No. 6 • November 2006
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