On the Cluster Size Distribution for Percolation on Some General Graphs
Artikel i vetenskaplig tidskrift, 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.