On the cluster size distribution for percolation on some general graphs
Rev. Mat. Iberoamericana, Tome 26 (2010) no. 1, p. 529-550 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
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.
Publié le : 2010-06-15
Classification:  amenability,  Cayley graphs,  cluster size distribution,  exponential decay,  percolation,  sub-exponential decay,  60K35,  82B43 
@article{1275671310,
     author = {Bandyopadhyay
, 
Antar and Steif
, 
Jeffrey and Tim\'ar
, 
\'Ad\'am},
     title = {On the cluster size distribution for percolation on some general graphs},
     journal = {Rev. Mat. Iberoamericana},
     volume = {26},
     number = {1},
     year = {2010},
     pages = { 529-550},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1275671310}
}

Bandyopadhyay
, 
Antar; Steif
, 
Jeffrey; Timár
, 
Ádám. On the cluster size distribution for percolation on some general graphs. Rev. Mat. Iberoamericana, Tome 26 (2010) no. 1, pp.  529-550. http://gdmltest.u-ga.fr/item/1275671310/