Revista Matemática Iberoamericana
- Rev. Mat. Iberoamericana
- Volume 26, Number 2 (2010), 529-550.
On the cluster size distribution for percolation on some general graphs
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.
Rev. Mat. Iberoamericana, Volume 26, Number 2 (2010), 529-550.
First available in Project Euclid: 4 June 2010
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Bandyopadhyay, Antar; Steif, Jeffrey; Timár, Ádám. On the cluster size distribution for percolation on some general graphs. Rev. Mat. Iberoamericana 26 (2010), no. 2, 529--550. https://projecteuclid.org/euclid.rmi/1275671310