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.

percolation

exponential decay

Cayley graph

Författare

Antar Bandyopadhyay

Indian Statistical Institute (Delhi Centre)

Jeffrey Steif

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

Adam Timar

Universität Bonn

Revista Matematica Iberoamericana

0213-2230 (ISSN)

Vol. 26 529-550

Ämneskategorier

Annan matematik