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

Understand

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.