- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:45
Revista Matemática Iberoamericana
Rev. Mat. Iberoamericana
RMI
0213-2230
2235-0616
General
10.4171/RMI
http://www.ems-ph.org/doi/10.4171/RMI
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2012)
26
2010
2
On the cluster size distribution for percolation on some general graphs
Antar
Bandyopadhyay
Indian Statistical Institute, NEW DELHI, INDIA
Jeffrey
Steif
Chalmers University of Technology, GOTHENBURG, SWEDEN
Ádám
Timár
Universität Bonn, BONN, GERMANY
Amenability, Cayley graphs, cluster size distribution, exponential decay, percolation, sub-exponential decay
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.
Probability theory and stochastic processes
Statistical mechanics, structure of matter
General
529
550
10.4171/RMI/608
http://www.ems-ph.org/doi/10.4171/RMI/608