We consider Bernoulli bond percolation on infinite graphs and we identify a class of graphs for which the critical percolation probability is strictly less than 1. The graphs in this class have to fulfill conditions stated in terms of a minimal cut set property and a logarithmic isoperimetric inequality. For the particular case of planar graphs the condition on minimal cut sets can be be replaced by the assumption that the dual of the graph is bounded degree.

Procacci, A., Scoppola, B. (2004). Infinite graphs with a nontrivial bond percolation threshold: Some sufficient conditions. JOURNAL OF STATISTICAL PHYSICS, 115, 1113-1127 [10.1023/B:JOSS.0000022369.76414.33].

Infinite graphs with a nontrivial bond percolation threshold: Some sufficient conditions

SCOPPOLA, BENEDETTO
2004-01-01

Abstract

We consider Bernoulli bond percolation on infinite graphs and we identify a class of graphs for which the critical percolation probability is strictly less than 1. The graphs in this class have to fulfill conditions stated in terms of a minimal cut set property and a logarithmic isoperimetric inequality. For the particular case of planar graphs the condition on minimal cut sets can be be replaced by the assumption that the dual of the graph is bounded degree.
2004
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore MAT/07 - FISICA MATEMATICA
English
Con Impact Factor ISI
Infinite graphs; Peierls argument; Percolation
Procacci, A., Scoppola, B. (2004). Infinite graphs with a nontrivial bond percolation threshold: Some sufficient conditions. JOURNAL OF STATISTICAL PHYSICS, 115, 1113-1127 [10.1023/B:JOSS.0000022369.76414.33].
Procacci, A; Scoppola, B
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/32991
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