- 03-501 Aldo Procacci, Benedetto Scoppola
- Infinite graphs with a nontrivial bond percolation threshold:
some sufficient conditions.
Nov 14, 03
(auto. generated ps),
of related papers
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.