Giovanni Conforti (École Polytechnique):
Title: The dynamics of Schrodinger bridges
Schroedinger bridges (SB) allow to lift from the point to the mesure setting the concept of Brownian bridge. On the other hand, they arise naturally as the critical curve for the dynamic formulation of the regularized Monge-Kantorovich problem. In this talk I will present some recently obtained results for the dynamics of Schroedinger bridges. In particular, I will show that the marginal flow of SB may be interpreted as Newton’s law, where the acceleration field is given by the gradient of the Fisher information. With this interpretation at hand, one we study the evolution of the entropy along the marginal flow, and provide sharp estimates. As a by product we get an entropic inequality for the entropic transportation cost. The results we obtain allow to recover, in the short-time limit, the well known convexity of the entropy along displacement interpolations. If time allows, I will also discuss the evolution of the fisher information along SB.