160 citations · 367 across the 20 of their papers we have counts for
25 papers
Monge-Ampère gravity, optimal transport theory and their link to the Galileons
Albert Bonnefous, Yann Brenier, Roya Mohayaee
Mathematicians have been proposing for sometimes that Monge-Ampère equation, a nonlinear generalization of the Poisson equation, where trace of the Hessian is replaced by its deter…
Monge Ampère gravity: from the large deviation principle to cosmological simulations through optimal transport
Bruno Lévy, Yann Brenier, Roya Mohayaee
We study Monge-Ampère gravity (MAG) as an effective theory of cosmological structure formation through optimal transport theory. MAG is based on the Monge-Ampère equation, a nonlin…
Relaxed solutions for incompressible inviscid flows: A variational and gravitational approximation to the initial value problem
Yann Brenier, Iván Moyano
Following Arnold's geometric interpretation, the Euler equations of an incompressible fluid moving in a domain D are known to be the optimality equation of the minimizing geodesic…
-convergence for a class of action functionals induced by gradients of convex functions
Luigi Ambrosio, Aymeric Baradat, Yann Brenier
Given a real function , the rate function for the large deviations of the diffusion process of drift given by the Freidlin-Wentzell theorem coincides with the time in…
Monge-Ampère gravitation as a -limit of good rate functions
Luigi Ambrosio, Aymeric Baradat, Yann Brenier
Monge-Ampère gravitation is a modification of the classical Newtonian gravitation where the linear Poisson equation is replaced by the nonlinear Monge-Ampère equation. This paper i…
On optimal transport of matrix-valued measures
Yann Brenier, Dmitry Vorotnikov
We suggest a new way of defining optimal transport of positive-semidefinite matrix-valued measures. It is inspired by a recent rendering of the incompressible Euler equations and r…