Research

In general, my research focuses on the study and development of theoretical tools for establishing limit theorems in probability theory, identifying metrics guaranteeing these convergences, and studying the finer properties of limit laws such as the existence and regularity of a density, the support, or concentration. To do this, I use and develop tools such as Malliavin calculus, Dirichlet forms, and Stein's method. These tools essentially allow for setting up a differential calculus for studying the considered laws, which proves useful, notably for establishing the existence of densities or the convergence of these densities for suitable sequences of random variables.

The random variables I primarily study using the aforementioned tools are Wiener chaos. Indeed, any sufficiently integrable random variable admits a decomposition into chaos, and a thorough understanding of the properties of chaotic random variables indirectly allows for studying general random variables that are not necessarily chaotic. As an example, I particularly study nodal random variables, which are obtained as the volume of the zero set of a certain stochastic process typically Gaussian (random polynomials, Gaussian processes in Euclidean spaces, random combinations of eigenfunctions of the Laplacian on a manifold, etc.). When removing the Gaussianity assumption or when introducing some kind of randomness, verifying whether the asymptotic phenomena established in the Gaussian case persists for other kind of strong dependence, i.e., testing their universality properties, is at the heart of my recent work.