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Neighboring clusters in Bernoulli percolation

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

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Adám Timár. 2007-02-28. Neighboring clusters in Bernoulli percolation. https://doi.org/10.1214/009117906000000485

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