Monge-Ampère gravitation as a Γ-limit of good rate functions
Résumé
Monge-Ampère gravitation is a modification of the classical Newtonian gravitation where the linear Poisson equation is replaced by the nonlinear Monge-Ampère equation. This paper is concerned with the rigorous derivation of Monge-Ampère gravitation for a finite number of particles from the stochastic model of a Brownian point cloud, in the spirit of the formal paper [6]. The main step in this derivation is the Γ−convergence of the good rate functions corresponding to a one-parameter family of large deviation principles. Surprisingly, the derived model includes dissipative phenomena. As an illustration, we show that it leads to sticky collisions in one space dimension.
Domaines
Mathématiques [math]
Origine : Fichiers produits par l'(les) auteur(s)