Neighboring clusters in bernoulli percolation

Adám Timár*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)2332-2343
Number of pages12
JournalAnnals of Probability
Issue number6
Publication statusPublished - Nov 2006

Other keywords

  • Cluster repulsion
  • Nonamenable
  • Percolation
  • Touching clusters


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