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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-Amp\`ere gravitation is a modification of the classical Newtonian gravitation where the linear Poisson equation is replaced by the nonlinear Monge-Amp\`ere equation. This paper is concerned with the rigorous derivation of Monge-Amp\`ere gravitation for a finite number of particles from the stochastic model of a Brownian point cloud, in the spirit of a previous work by the third author [A double large deviation principle for Monge-Amp\`ere gravitation, 2016]. The main step in this derivation is the Γconvergence 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-04308792 , version 1 (17-09-2024)

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Luigi Ambrosio, Aymeric Baradat, Yann Brenier. Monge–Ampère gravitation as a Γ-limit of good rate functions. Analysis & PDE, 2023, 16 (9), pp.2005-2040. ⟨10.2140/apde.2023.16.2005⟩. ⟨hal-04308792⟩
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