A double large deviation principle for monge-ampere gravitation

2015/04/23 by Yann Brenier, Brenier, Yann
Engineering · Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Cosmology and Gravitation Theories #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Gas Dynamics and Kinetic Theory

paper · pdf · doi:10.48550/arxiv.1504.07583

openalex publication_date 2015/04/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Monge-Ampere gravitation is a nonlinear modification of classical Newtonian gravitation, when the Monge-Ampere equation substitutes for the Poisson equation. We establish, through two applications of the large deviation principle, that the MA gravitation for a finite number of particles can be reduced, through a double application of the large deviation principle, to the simplest possible stochastic model: a collection of independent Brownian motions with vanishing noise.

Citations

• The Feynman Lectures on Physics
• From the Schrödinger problem to the Monge–Kantorovich problem
• Polar factorization and monotone rearrangement of vector‐valued functions
• Reconstruction of the early Universe as a convex optimization problem

Related

• Monge Ampère gravity: from the large deviation principle to cosmological simulations through optimal transport
• Monge-Ampère gravity, optimal transport theory and their link to the Galileons
• Alternative approach to gravity and MOND
• Leading Logarithm Quantum Gravity
• Deviation of Large Scale Gravitoelectromagnetic Field in Post-Newtonian Approximation