From the Schrödinger problem to the Monge-Kantorovich problem. An entropic approach to optimal transport.

  • Christian Léonard (Université Paris Ouest, Nanterre, France)
Raum n.n. Universität Leipzig (Leipzig)


In the early 30's, Schrödinger addressed and solved formally a statistical physics problem which is amazingly analogous to quantum mechanics. It is a large deviation problem which is similar to the Monge-Kantorovich optimal transport problem. This similarity is not incidental. Indeed, it will be shown that the optimal transport problem is the limit of a sequence of well-chosen Schrödinger problems. Analytically, this amounts to describe the optimal transport problem as a Gamma-limit of relative entropy minimization problems under prescribed marginal constraints. The minimizers of these problems might be interpreted as some kind of geodesics in the space of probability measures.


8/2/10 8/6/10

Information Geometry and its Applications III

Universität Leipzig Raum n.n.

Antje Vandenberg

Max-Planck-Institut für Mathematik in den Naturwissenschaften Contact via Mail

Nihat Ay

Max Planck Institute for Mathematics in the Sciences, Germany

Paolo Gibilisco

Università degli Studi di Roma "Tor Vergata", Italy

František Matúš

Academy of Sciences of the Czech Republic, Czech Republic