Concentration for Coulomb gases and Coulomb transport inequalities
Mathematical Physics Seminar
17th November 2017, 2:00 pm – 3:00 pm
Howard House, 4th Floor Seminar Room
We study the non-asymptotic behavior of Coulomb gases in dimension two and more. Such gases are important examples in statistical mechanics arising in several contexts. From the probabilistic point of view, they are modeled by an exchangeable Boltzmann-Gibbs measure with a singular two-body interaction. We obtain concentration of measure inequalities for the empirical distribution of such gases around their equilibrium measure. Our approach is remarkably simple and bypasses the use of renormalized energy. It relies on new inequalities between probability metrics, including Coulomb transport inequalities which will be presented in the talk. This is based on a joint work with Djalil Chafaï (Dauphine) and Adrien Hardy (Lille).