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A double large deviation principle for monge-ampere gravitation

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.