Section: New Results

Concentration for Coulomb gases and Coulomb transport inequalities

The convergence of the Coulomb gas, which is a statistical gas of charged particles in an electrostatic interaction, towards its limiting distribution as the number of particles goes to infinity is a result which is part of the folklore of potential theory. The speed at which this convergence arise, which can be assessed through concentration of measure estimates in, say, the Wasserstein-Kantorovich metric, are however new results obtained by D. Chafaï, A. Hardy and M. Maïda in [7]. One of the main ingredient was to develop transport inequalities associated with the Coulomb interaction.