Neighboring clusters in Bernoulli percolation

Details Neighboring clusters in Bernoulli percolation Neighboring clusters in Bernoulli percolation

2007-02-28

arxiv.org/abs/math/0702873v1

Annals of Probability 2006, Vol. 34, No. 6, 2332-2343

Mathematics

Probability

Published at http://dx.doi.org/10.1214/009117906000000485 in the Annals of Probability (http://www.imstat.org/aop/) by the Ins

Scientific paper

10.1214/009117906000000485

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
H\"{a}ggstr\"{o}m, Peres and Schonmann.

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