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Article Dans Une Revue Analysis & PDE Année : 2023

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.
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Dates et versions

hal-04059631 , version 1 (05-04-2023)

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Luigi Ambrosio, Aymeric Baradat, Yann Brenier. Monge-Ampère gravitation as a Γ-limit of good rate functions. Analysis & PDE, In press, ⟨10.48550/arXiv.2002.11966⟩. ⟨hal-04059631⟩
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