Percolation, Perimetry, Planarity

Mathematics – Probability

Scientific paper

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5 pages. New version includes a proof of the existence of a dual graph of the type necessary for the proof. Accepted to Rev. M

Scientific paper

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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