Orateur
Description
This talk is concerned with the empirical measure of a random point process in R^d, such as the eigenvalues of a random matrix or a Coulomb gas. In several cases, this empirical measure converges towards a deterministic measure. In order to quantify the rate of convergence, we are interested in the p-Wasserstein distance between this random measure and its mean, particularly in dimension 2. We obtain a bound for this distance under some assumption on the p-th centered moment of the number of points in squares, which amounts to hyperuniformity when p=2. In addition, hyperuniform determinantal point processes will satisfy the required assumptions for any p>=1.
This is a joint work with Raphaël Butez (Université de Lille) and David García-Zelada (Sorbonne Université).
