This paper exploit the equivalence between the Schrödinger Bridge problem (Léonard in J
Funct Anal 262: 1879–1920, 2012; Nelson in Phys Rev 150: 1079, 1966; Schrödinger in …

We investigate the convergence rate of the optimal entropic cost v ε to the optimal transport
cost as the noise parameter ε↓ 0. We show that for a large class of cost functions c on R d× …

We devise a theoretical framework and a numerical method to infer trajectories of a
stochastic process from samples of its temporal marginals. This problem arises in the …

Starting from Brenier's relaxed formulation of the incompressible Euler equation in terms of
geodesics in the group of measure-preserving diffeomorphisms, we propose a numerical …

We present a stochastic Lagrangian view of fluid dynamics. The velocity solving the
deterministic Navier–Stokes equation is regarded as a mean time derivative taken over …

We propose an entropy minimization viewpoint on variational mean-field games with
diffusion and quadratic Hamiltonian. We carefully analyze the time discretization of such …

This paper is concerned with six variational problems and their mutual connections: the
quadratic Monge–Kantorovich optimal transport, the Schrödinger problem, Brenier's relaxed …

What is the suitable Laplace operator on vector fields for the Navier-Stokes equation on a
Riemannian manifold? In this note, by considering Nash embedding, we will try to elucidate …

We present a stylized model of controlled equilibration of a small system in a fluctuating
environment. We derive the optimal control equations steering in finite-time the system …

In this paper we introduce a (partly) new approach for the study of McKean-Vlasov
equations, including singular interactions. This approach is based on the relativeentropy on …