A large deviation principle for a natural sequence of point processes on a Riemannian two-dimensional manifold

Abstract

We follow the techniques of Paul Dupuis, Vaios Laschos, and Kavita Ramanan in [8] to prove a large deviation principle for a sequence of point processes dened by Gibbs measures on a compact orientable two- dimensional Riemannian manifold. We see that the corresponding sequence of empirical measures converges to the solution of a partial differential equation and, in some cases, to the volume form of a constant curvature metric.