Large-N asymptotic expansion for mean field models with Coulomb gas interaction

Abstract

We derive the large-N, all order asymptotic expansion for a system of N particles with mean-field interactions on top of a Coulomb repulsion at temperature 1/β, under the assumptions that the interactions are analytic, off-critical, and satisfy a local strict convexity assumption.

52 pages ; v2 : change of title, references added + some more details in the proof of regularity (Section 7)