Séminaires : Séminaire d'Analyse Fonctionnelle

Equipe(s) : af,
Responsables :E. Abakoumov - A.Eskenazis - D. Cordero-Erausquin - M. Fathi - O. Guédon - B. Maurey
Email des responsables :
Salle : salle 13 - couloir 15-16 - 4ème étage
Adresse :Campus Pierre et Marie Curie
Le Jeudi à 10h30 -  IMJ-PRG - 4 place Jussieu - 75005 PARIS

Orateur(s) Djalil Chafai - Dauphine,
Titre Concentration for Coulomb gases and Coulomb transport inequalities
Horaire10:30 à 11:30
RésumeThis 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.«»
Sallesalle 13 - couloir 15-16 - 4ème étage
AdresseCampus Pierre et Marie Curie