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June, 2010 On the cluster size distribution for percolation on some general graphs
Antar Bandyopadhyay , Jeffrey Steif , Ádám Timár
Rev. Mat. Iberoamericana 26(2): 529-550 (June, 2010).

Abstract

We show that for any Cayley graph, the probability (at any $p$) that the cluster of the origin has size $n$ decays at a well-defined exponential rate (possibly 0). For general graphs, we relate this rate being positive in the supercritical regime with the amenability/nonamenability of the underlying graph.

Citation

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Antar Bandyopadhyay . Jeffrey Steif . Ádám Timár . "On the cluster size distribution for percolation on some general graphs." Rev. Mat. Iberoamericana 26 (2) 529 - 550, June, 2010.

Information

Published: June, 2010
First available in Project Euclid: 4 June 2010

zbMATH: 1203.60142
MathSciNet: MR2677006

Subjects:
Primary: 60K35, 82B43

Rights: Copyright © 2010 Departamento de Matemáticas, Universidad Autónoma de Madrid

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Vol.26 • No. 2 • June, 2010
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