Publications and Preprints

On the cluster size distribution for percolation on some general graphs
Antar Bandyopadhyay, Jeffrey Steif and dm Timr
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.

isid/ms/2008/03 [fulltext]

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