6 citations · 13 across the 10 of their papers we have counts for
12 papers
Multiphasic formulation of Vlasov equations and applications
Aymeric Baradat, Lucas Ertzbischoff, Daniel Han-Kwan
This work is a mathematical study of the multiphasic formulation of the Vlasov equation, which consists in recasting this collisionless kinetic equation as a system of coupled pres…
A convergence rate for the entropic JKO scheme
Aymeric Baradat, Sofiane Cherf
The so-called JKO scheme, named after Jordan, Kinderlehrer and Otto, provides a variational way to construct discrete time approximations of certain partial differential equations…
Using Sinkhorn in the JKO scheme adds linear diffusion
Aymeric Baradat, Anastasiia Hraivoronska, Filippo Santambrogio
The JKO scheme is a time-discrete scheme of implicit Euler type that allows to construct weak solutions of evolution PDEs which have a Wasserstein gradient structure. The purpose o…
Convergence of the Sinkhorn algorithm when the Schrödinger problem has no solution
Aymeric Baradat, Elias Ventre
The Sinkhorn algorithm is the most popular method for solving the entropy minimization problem called the Schrödinger problem: in the non-degenerate cases, the latter admits a uniq…
Regularized unbalanced optimal transport as entropy minimization with respect to branching Brownian motion
Aymeric Baradat, Hugo Lavenant
We consider the problem of minimizing the entropy of a law with respect to the law of a reference branching Brownian motion under density constraints at an initial and final time.…
-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…
Minimizing relative entropy of path measures under marginal constraints
Aymeric Baradat, Christian Léonard
We study generalizations of the Schrödinger problem in statistical mechanics in two directions: when the density is constrained at more than two times, and when the joint law of th…
Nonlinear instability in Vlasov type equations around rough velocity profiles
Aymeric Baradat
In the Vlasov-Poisson equation, every configuration which is homogeneous in space provides a stationary solution. Penrose gave in 1960 a criterion for such a configuration to be li…
Small noise limit and convexity for generalized incompressible flows, Schrödinger problems, and optimal transport
Aymeric Baradat, Léonard Monsaingeon
This paper is concerned with six variational problems and their mutual connections: The quadratic Monge-Kantorovich optimal transport, the Schrödinger problem, Brenier's relaxed mo…
On the existence of a scalar pressure field in the Brödinger problem
Aymeric Baradat
This work deals with the entropic regularization of the Brenier problem for perfect incompressible fluids introduced by Arnaudon, Cruzeiro, Léonard and Zambrini. We show that as in…
Continuous dependence of the pressure field with respect to endpoints for ideal incompressible fluids
Aymeric Baradat
In the Brenier variational model for perfect fluids, the datum is the joint law of the initial and final positions of the particles. In this paper, we show that both the optimal ac…