Neighboring clusters in Bernoulli percolation

DOI10.1214/009117906000000485zbMATH Open1112.60085arXivmath/0702873OpenAlexW2036575730MaRDI QIDQ874738

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Publication date: 10 April 2007

Published in: (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/math/0702873

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