On the Cluster Size Distribution for Percolation on Some General Graphs
Probability
2008-05-26 v1 Mathematical Physics
math.MP
Abstract
We show that for any Cayley graph, the probability (at any ) 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.
Keywords
Cite
@article{arxiv.0805.3620,
title = {On the Cluster Size Distribution for Percolation on Some General Graphs},
author = {Antar Bandyopadhyay and Jeffrey Steif and Adam Timar},
journal= {arXiv preprint arXiv:0805.3620},
year = {2008}
}
Comments
22 pages