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Extremal Curves in Wasserstein Space

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Geometric Science of Information (GSI 2017)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 10589))

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Abstract

We show that known Newton-type laws for Optimal Mass Transport, Schrödinger Bridges and the classic Madelung fluid can be derived from variational principles on Wasserstein space. The second order differential equations are accordingly obtained by annihilating the first variation of a suitable action.

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Notes

  1. 1.

    \(\mu _k\) converges weakly to \(\mu \) if \(\int _{{\mathbb R}^N}fd\mu _k\rightarrow \int _{{\mathbb R}^N}fd\mu \) for every continuous, bounded function f.

  2. 2.

    The case of a general reversible Markovian prior is treated in [14] where all the details of the variational analysis may also be found.

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Author information

Authors and Affiliations

  1. Laboratoire Paul Painlevé, Université des Sciences et Technologies de Lille 1, 59655, Villeneuve d’Ascq Cedex, France

    Giovanni Conforti

  2. Dipartimento di Matematica “Tullio Levi-Civita”, Università di Padova, via Trieste 63, 35121, Padova, Italy

    Michele Pavon

Authors
  1. Giovanni Conforti
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  2. Michele Pavon
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Correspondence to Michele Pavon .

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Editors and Affiliations

  1. Ecole Polytechnique, Palaiseau, France

    Frank Nielsen

  2. Thales Land and Air Systems, Limours, France

    Frédéric Barbaresco

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Conforti, G., Pavon, M. (2017). Extremal Curves in Wasserstein Space. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2017. Lecture Notes in Computer Science(), vol 10589. Springer, Cham. https://doi.org/10.1007/978-3-319-68445-1_11

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  • DOI: https://doi.org/10.1007/978-3-319-68445-1_11

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