Entropic and optimal transport

The Schrödinger problem is an entropy minimization problem on a set of path measures with prescribed initial and final marginals. It arises from a large deviation principle for the empirical measures of large particle systems. When the dynamics of the particles is slowed down while the prescribed marginals are unchanged, a second level large deviation phenomenon occurs. This leads to a sequence, indexed by the slowdown parameter, of Schrödinger problems Gamma-converging to a dynamical optimal transport problem.

Invited by Sylvie Roelly.