Percolation, Perimetry, Planarity
Probability
2007-05-23 v2 Combinatorics
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<1.
Keywords
Cite
@article{arxiv.math/0509235,
title = {Percolation, Perimetry, Planarity},
author = {Gady Kozma},
journal= {arXiv preprint arXiv:math/0509235},
year = {2007}
}
Comments
5 pages. New version includes a proof of the existence of a dual graph of the type necessary for the proof. Accepted to Rev. Math. Iberoamericana