Neighboring clusters in Bernoulli percolation
arXiv:math/0702873 · doi:10.1214/009117906000000485
Abstract
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.
Published at http://dx.doi.org/10.1214/009117906000000485 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)