# The dynamics of Schroedinger bridges.

 Orateur: Giovanni CONFORTI Localisation: École polytechnique, France Type: Groupe de travail Convexité, Transport Optimal et Probabilités (CTOP) Site: Hors LAMA , IHP Salle: 01 Date de début: 23/11/2017 - 14:00 Date de fin: 23/11/2017 - 17:00

A Schroedinger bridge is a stochastic process which provides with a probabilistic version of the displacement interpolation between probability measures. In this talk I will start by surveying the parallelism between the Schroedinger problem and the Monge-Kantorovich problem. Next, I will present some recently obtained results for the dynamics of Schroedinger bridges. In particular, I will discuss an equation for the marginal flow, quantitative bounds for the evolution of the marginal entropy, and provide some applications. Finally, I will outline some connections between the so called reciprocal characteristics” of a Langevin dynamics and the convexity of the Fisher information.