Neighboring clusters in Bernoulli percolation

• Adám Timár ^[1]
  1. [1] Indiana University
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 34, Nº. 6, 2006, págs. 2332-2343
• Idioma: inglés
• DOI: 10.1214/009117906000000485
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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.