Volume 8 (2025)
Vanneuville, Hugo
Exponential decay of the volume for Bernoulli percolation: a proof via stochastic comparison
Annales Henri Lebesgue, Volume 8 (2025), pp. 101-112.

Metadata

DOI10.5802/ahl.230
Keywords Percolation, sharpness, stochastic comparison

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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