On the Cluster Size Distribution for Percolation on Some General Graphs
نویسندگان
چکیده
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. AMS 2000 subject classification: 60K35, 82B43
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