Exponential decay of the volume for Bernoulli percolation: a proof via stochastic comparison

2023/04/24 by Hugo Vanneuville, Vanneuville, Hugo · 4 citations
Mathematics · Physics and Astronomy · #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.2304.12110

openalex publication_date 2023/04/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let us consider subcritical Bernoulli percolation on a connected, transitive, infinite and locally finite graph. In this paper, we propose a new (and short) proof of the exponential decay property for the volume of clusters. We do not rely on differential inequalities and rather use stochastic comparison techniques, which are inspired by several works including the paper "An approximate zero-one law" written by Russo in the early eighties.

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