On the Cluster Size Distribution for Percolation on Some General Graphs
Journal article, 2010

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.


exponential decay

Cayley graph


Antar Bandyopadhyay

Indian Statistical Institute (Delhi Centre)

Jeffrey Steif

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

Adam Timar

University of Bonn

Revista Matematica Iberoamericana

0213-2230 (ISSN)

Vol. 26 2 529-550

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Other Mathematics

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