The Annals of Probability
- Ann. Probab.
- Volume 34, Number 6 (2006), 2332-2343.
Neighboring clusters in Bernoulli percolation
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.
Ann. Probab., Volume 34, Number 6 (2006), 2332-2343.
First available in Project Euclid: 13 February 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 82B43: Percolation [See also 60K35]
Secondary: 60B99: None of the above, but in this section
Timár, Adám. Neighboring clusters in Bernoulli percolation. Ann. Probab. 34 (2006), no. 6, 2332--2343. doi:10.1214/009117906000000485. https://projecteuclid.org/euclid.aop/1171377445