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arxiv: math/0509235 · v2 · submitted 2005-09-10 · 🧮 math.PR · math.CO

Percolation, Perimetry, Planarity

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keywords percolationbernoullibiggercriticaldimensiongraphgrowthisoperimetric
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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.

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