Nils Berglund (Université d’Orléans) 

Abstract

Wiener chaos (or polynomial chaos) expansion is a way to represent random variables as polynomials of Gaussianrandom variables. It links fundamental concepts in probability, statistics, and physics, such as Hermitepolynomials, cumulant expansions, Isserlis/Wick calculus, the Gaussian free field, the quantum harmonic oscillator,Fock space, and Feynman diagrams.The lectures will start with the case of one-dimensional normal variables, assuming only elementary knowledge on continuous random variables. They will then explore someof the above connections, first for finite-dimensional multivariate Gaussians, and then for Gaussian fields.