The OSSS Method in Percolation Theory

Abstract

In 2017, Duminil-Copin et al. introduced the OSSS method to study properties of diverse percolation models. This document aims to introduce the reader to this new method. It contains a introduction to percolation theory, then concentrates on the case of Poisson-Boolean percolation. The majority of this document is dedicated to an detailed analysis of [DRT18]. This work is the result of an internship in Summer 2019 with Jean-Baptiste Gouéré at the University of Tours.

References in corpus (2)

• Exponential decay of connection probabilities for subcritical Voronoi percolation in ${\mathbb{R}}^d$
• Sixty years of percolation