A large deviation principle for weighted Riesz interactions

Abstract

We prove a large deviation principle for the sequence of push-forwards of empirical measures in the setting of Riesz potential interactions on compact subsets $K$ in $R^d$ with continuous external fields. Our results are valid for base measures on $K$ satisfying a strong Bernstein-Markov type property for Riesz potentials. Furthermore, we give sufficient conditions on K (which are satisfied if $K$ is a smooth submanifold) so that a measure on $K$ which satisfies a mass-density condition will also satisfy this strong Bernstein-Markov property.