A large deviation principle for empirical measures on Polish spaces

by David García Zelada (Université Paris Dauphine)

Location: 200B.02.18, Leuven
Time: Tuesday January 29, 2019 at 16:00

We will be interested in a model of n interacting particles at positive temperature. Its macroscopic behavior as n grows to infinity will be studied by injecting, modulo permutations, the n-particle space into the space of probability measures. More specifically, we can prove a Laplace principle or, equivalently, a large deviation principle which implies, in some cases, an almost sure convergence to a deterministic probability measure. Among the usual models we can find the eigenvalue distribution of Gaussian random matrices and the roots of Gaussian random polynomials but the result allows us to study Coulomb gases on Riemannian manifolds as well. This talk is based on arXiv:1703.02680.