Mean-field limits for Riesz systems

Matt Rosenzweig, Carnegie Mellon University
Fine Hall 314

InĀ statistical physics, many particle models are described by an interaction energy determined by the Coulomb potential, or more generally an inverse power law called a Riesz potential. I will discuss the interplay of entropy, energy, and functional inequalities in establishing the mean-field convergence/propagation of chaos for the dynamics of such interacting particle systems. I will also discuss the role of the trend to equilibrium for the mean-field equation and how it allows to deduce uniform-in-time convergence results or even establish the generation of chaos.