Percolation, Perimetry, Planarity

2005/09/10 by Gady Kozma, Kozma, Gady
Mathematics · Physics and Astronomy · #05C10 #60K35 #82B43 #Combinatorics (math.CO) #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.math/0509235

openalex publication_date 2005/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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