Information Geometry and its Applications III

Abstract Christian Léonard

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Christian Léonard  (Université Paris Ouest, France)
Monday, August 02, 2010, room Hörsaal 1
From the Schrödinger problem to the Monge-Kantorovich problem. An entropic approach to optimal transport.

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.

Date and Location

August 02 - 06, 2010
University of Leipzig
04103 Leipzig

Scientific Organizers

Nihat Ay
Max Planck Institute for Mathematics in the Sciences
Information Theory of Cognitive Systems Group
Contact by Email

Paolo Gibilisco
Università degli Studi di Roma "Tor Vergata"
Facoltà di Economia
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František Matúš
Academy of Sciences of the Czech Republic
Institute of Information Theory and Automation
Czech Republic
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Scientific Committee

Shun-ichi Amari
Brain Science Institute, Mathematical Neuroscience Laboratory
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Imre Csiszár
Hungarian Academy of Sciences
Alfréd Rényi Institute of Mathematics
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Dénes Petz
Budapest University of Technology and Economics
Department for Mathematical Analysis
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Giovanni Pistone
Collegio Carlo Alberto, Moncalieri
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Administrative Contact

Antje Vandenberg
Max Planck Institute for Mathematics in the Sciences
Contact by Email
Phone: (++49)-(0)341-9959-552
Fax: (++49)-(0)341-9959-555

05.04.2017, 12:42