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Some Geometric Consequences of the Schrödinger Problem

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Geometric Science of Information (GSI 2015)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 9389))

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Abstract

This note presents a short review of the Schrödinger problem and of the first steps that might lead to interesting consequences in terms of geometry. We stress the analogies between this entropy minimization problem and the renowned optimal transport problem, in search for a theory of lower bounded curvature for metric spaces, including discrete graphs.

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Author information

Authors and Affiliations

  1. Modal-X, Université Paris Ouest, Bât. G, 200 av. de la République, 92001, Nanterre, France

    Christian Léonard

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  1. Christian Léonard
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Correspondence to Christian Léonard .

Editor information

Editors and Affiliations

  1. Bâtiment Alan Turing, CS35003, École Polytechnique, Palaiseau, France

    Frank Nielsen

  2. Thales Land\& Air Systems, Limours, France

    Frédéric Barbaresco

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Léonard, C. (2015). Some Geometric Consequences of the Schrödinger Problem. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2015. Lecture Notes in Computer Science(), vol 9389. Springer, Cham. https://doi.org/10.1007/978-3-319-25040-3_7

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  • DOI: https://doi.org/10.1007/978-3-319-25040-3_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-25039-7

  • Online ISBN: 978-3-319-25040-3

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