Percolation, perimetry, planarity. (English) Zbl 1131.60087

Summary: Let \(G\) be a planar graph with polynomial growth and isoperimetric dimension bigger than 1. Then the critical \(p\) for Bernoulli percolation on \(G\) satisfies \(p_{c} < 1\).


60K35 Interacting random processes; statistical mechanics type models; percolation theory
82B43 Percolation
05C10 Planar graphs; geometric and topological aspects of graph theory
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