“Exponential Decay in Percolation: A proof using Pivotality”
Martedì 3 Giugno 2025, ore 17:00 - Aula 2AB45 - Felix Rouveyre (PhD Student Université Aix-Marseille)
Abstract
We consider independent Bernoulli bond percolation with parameter p on the d-dimensional cubic lattice. In the subcritical regime – that is, for sufficiently small values of p – the size of any cluster is known to be almost surely finite, and the probability that a cluster reaches a given size decays exponentially fast. In this talk, I will present a recent and concise proof of this exponential decay, due to Hugo Vanneuville (2024). The proof relies on stochastic comparison techniques, originally developed by Russo in the 1980s, using the notion of pivotality. I aim to provide a general and accessible overview of these techniques.
