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arXiv · 0805.3620

On the Cluster Size Distribution for Percolation on Some General Graphs

Antar Bandyopadhyay·Jeffrey Steif·Adam Timar
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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.

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Antar Bandyopadhyay, Jeffrey Steif, Adam Timar. 2008-05-23. On the Cluster Size Distribution for Percolation on Some General Graphs. https://arxiv.org/abs/0805.3620

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