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On the Cluster Size Distribution for Percolation on Some General Graphs

Antar Bandyopadhyay ; Jeffrey Steif (Institutionen för matematiska vetenskaper, matematik) ; Adam Timar
Revista Matematica Iberoamericana (0213-2230 ). Vol. 26 (2010), p. 529-550.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: percolation, Cayley graph, exponential decay

Denna post skapades 2010-12-01. Senast ändrad 2015-07-02.
CPL Pubid: 129940


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Institutionen för matematiska vetenskaper, matematik (2005-2016)


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