Percolation, Perimetry, Planarity
Abstract
Description
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.
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
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