Monge-Ampère gravitation as a Γ-limit of good rate functions (Aymeric Baradat, ICJ Lyon)

Monge-Ampère gravitation is a modification of the classical Newtonian gravitation where the linear Poisson equation is replaced by the nonlinear Monge-Ampère equation. In this presentation, I will explain how to derive a model where a finite number of particles interact according to Monge-Ampère gravitation, starting from the basic model of indistinguishable Brownian particles. I will proceed in two steps. First, I will study a large deviation problem related to this model at fixed positive diffusivity, and then I will show that this problem converges when the diffusivity tends to zero. The limiting problem corresponds to minimizing a singular Lagrangian encoding Monge-Ampère gravitation. In addition, its singularities lead to sticky collisions in dimension 1. This is a joint work with Y. Brenier and L. Ambrosio.