On the Cluster Size Distribution for Percolation on Some General Graphs
Journal article, 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
Author
Antar Bandyopadhyay
Indian Statistical Institute (Delhi Centre)
Jeffrey Steif
Chalmers, Mathematical Sciences, Mathematics
University of Gothenburg
Adam Timar
University of Bonn
Revista Matematica Iberoamericana
0213-2230 (ISSN) 22350616 (eISSN)
Vol. 26 2 529-550Subject Categories
Other Mathematics
DOI
10.4171/RMI/608