Critical Percolation on Any Nonamenable Group has no Infinite Clusters
Benjamini, Itai ; Lyons, Russell ; Peres, Yuval ; Schramm, Oded
Ann. Probab., Tome 27 (1999) no. 1, p. 1347-1356 / Harvested from Project Euclid
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We show that independent percolation on any Cayley graph of a nonamenable group has no infinite components at the critical parameter. This result was obtained by the present authors earlier as a corollary of a general study of group-invariant percolation. The goal here is to present a simpler self-contained proof that easily extends to quasi-transitive graphs with a unimodular automorphism group. The key tool is a “mass-transport” method, which is a technique of averaging in nonamenable settings.
Publié le : 1999-07-14
Classification:  Percolation,  Cayley graphs,  amenability,  60B99,  60D05,  82B43 
@article{1022677450,
     author = {Benjamini, Itai and Lyons, Russell and Peres, Yuval and Schramm, Oded},
     title = {Critical Percolation on Any Nonamenable Group has no Infinite
		 Clusters},
     journal = {Ann. Probab.},
     volume = {27},
     number = {1},
     year = {1999},
     pages = { 1347-1356},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1022677450}
}

Benjamini, Itai; Lyons, Russell; Peres, Yuval; Schramm, Oded. Critical Percolation on Any Nonamenable Group has no Infinite
		 Clusters. Ann. Probab., Tome 27 (1999) no. 1, pp.  1347-1356. http://gdmltest.u-ga.fr/item/1022677450/