Neighboring clusters in Bernoulli percolation
Timár, Adám
Ann. Probab., Tome 34 (2006) no. 1, p. 2332-2343 / Harvested from Project Euclid
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We consider Bernoulli percolation on a locally finite quasi-transitive unimodular graph and prove that two infinite clusters cannot have infinitely many pairs of vertices at distance 1 from one another or, in other words, that such graphs exhibit “cluster repulsion.” This partially answers a question of Häggström, Peres and Schonmann.
Publié le : 2006-11-14
Classification:  Cluster repulsion,  percolation,  nonamenable,  touching clusters,  60K35,  82B43,  60B99 
@article{1171377445,
     author = {Tim\'ar, Ad\'am},
     title = {Neighboring clusters in Bernoulli percolation},
     journal = {Ann. Probab.},
     volume = {34},
     number = {1},
     year = {2006},
     pages = { 2332-2343},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1171377445}
}

Timár, Adám. Neighboring clusters in Bernoulli percolation. Ann. Probab., Tome 34 (2006) no. 1, pp.  2332-2343. http://gdmltest.u-ga.fr/item/1171377445/