Concentration for Coulomb gases and Coulomb transport inequalities

schedule le mardi 21 février 2017 de 16h30 à 17h30

Organisé par : Bastien Fernandez, Nicolas Fournier, Sandrine Péché

Intervenant : D. Chafaï (CEREMADE)
Lieu : Salle 0011, Sophie Germain (Université Paris Diderot)

Sujet : Concentration for Coulomb gases and Coulomb transport inequalities

Résumé :

This talk will present a joint work arXiv:1610.00980 with Mylène Maïda and Adrien Hardy on the non-asymptotic behavior of Coulomb gases in dimension two and more. Such gases are modeled by an exchangeable Boltzmann–Gibbs measure with a singular two-body interaction. Such measures are neither product  nor log-concave. We obtain concentration of measure inequalities for the empirical distribution of such gases around their equilibrium measure, with respect to bounded Lipschitz and Wasserstein distances. This implies macroscopic as well as mesoscopic convergence in such distances. In particular, we obtain for the first time a concentration inequality for the empirical spectral distribution of Ginibre random matrices. Our approach relies crucially on new inequalities between probability metrics, including Coulomb transport inequalities which can be of independent interest.