A Double Large Deviation Principle for Monge-Ampère Gravitation
by Yann Brenier  

Vol. 11 No. 1 (2016) P.23~P.41

ABSTRACT

Monge-Ampère gravitation is a nonlinear modification of classical Newtonian gravitation, when the Monge-Ampère 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.

KEYWORDS
Monge-Ampère, large deviation, gravitation.

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 35Q82, 49S05, 60F10.

MILESTONES

Received: 2015-03-31
Revised : 2015-07-08
Accepted: 2015-06-30

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