Séminaire Analyse-Proba (Hugo Vanneuville, mardi 9 décembre)

Le prochain séminaire Analyse-Proba aura lieu mardi 9 décembre à 10h30 en A711. Hugo Vanneuville (CNRS - Institut Fourier - Université Grenoble Alpes) nous parlera de :

Noise sensitivity for percolation

Abstract
Let us consider the hexagonal lattice, let us randomly color each hexagon independently black or white with probability 1/2, and look at percolation events (for example, the event that there is a black path from left to right in a large square). Benjamini, Kalai, and Schramm proved that percolation properties are noise sensitive, which means that if we introduce a ‘noise’ -- even very small -- to the colors of the hexagons, then the percolation events after and before the noise are quasi-independent of each other.
In this talk, we would like to propose a ‘robust’ approach -- i.e., one that extends to more general models, for example where the colors are not independent of each other -- to noise sensitivity. Unlike previous approaches, we do not rely on spectral tools but on differential inequalities satisfied by the probabilities of so-called ‘4-arm’ events, which are at the heart of Kesten's work in the 1980s and which we will define.
Joint work with Vincent Tassion.