Abstract
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 $p_{c} < 1$.
Citation
Gady Kozma. "Percolation, Perimetry, Planarity." Rev. Mat. Iberoamericana 23 (2) 671 - 676, August, 2007.
Information
Published: August, 2007
First available in Project Euclid: 26 September 2007
zbMATH: 1131.60087
MathSciNet: MR2371440
Subjects:
Primary:
46E15
Secondary:
46B99
,
46E35
Keywords:
Duality
,
isoperimetric dimension
,
percolation
,
planar graph
Rights: Copyright © 2007 Departamento de Matemáticas, Universidad Autónoma de Madrid
