From entropic to deterministic optimal transport

Por Christian Léonard (Univ. Paris Ouest).

Abstract: In the early 2000, T. Mikami proved the convergence of entropic transport to deterministic quadratic transport, when a fluctuation parameter vanishes, by means of h-processes. Inspired by some features of Mikami's method and applying elementary large deviation technics to the Schrödinger problem, we extend Mikami's result to any continuous cost function and recover the standard results about optimal transport without appealing to c-monotonicity.