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) 22350616 (eISSN)
Vol. 26 2 529-550Ämneskategorier
Annan matematik
DOI
10.4171/RMI/608