A DOUBLE LARGE DEVIATION PRINCIPLE FOR MONGE-AMPERE GRAVITATION

Yann Brenier (1)

1 CMLS - Centre de Mathématiques Laurent Schwartz

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.

Mots clés: Monge Ampere PDE; large deviation theory; optimal transport theory; Gravitation modifiée

Domaines: Mathématiques générales [math.GM]

Yann Brenier. A DOUBLE LARGE DEVIATION PRINCIPLE FOR MONGE-AMPERE GRAVITATION. 2015. ⟨hal-01137528⟩