Rate of convergence of empirical measures of hyperuniform point processes
Vienna Probability Seminar
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 Raphal Butez (Universit de Lille) and David Garca-Zelada (Sorbonne Universit).