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Non-monotone convergence in the quadratic Wasserstein distance

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Séminaire de Probabilités XLII

Part of the book series: Lecture Notes in Mathematics ((SEMPROBAB,volume 1979))

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Abstract

We give an easy counterexample to Problem 7.20 from C. Villani’s book on mass transport: in general, the quadratic Wasserstein distance between n-fold normalized convolutions of two given measures fails to decrease monotonically.

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References

  1. S. Artstein, K. M. Ball, F. Barthe and A. Naor, Solution of Shannon's Problem on the Monotonicity of Entropy, Journal of the AMS 17(4), 2004, pp. 975–982.

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Authors and Affiliations

  1. Vienna University of Technology, Wiedner Hauptstrasse, 8-10, A-1040, Vienna, Austria

    Walter Schachermayer

  2. Vienna University of Technology, Wiedner Hauptstrasse, 8-10, A-1040, Vienna, Austria

    Uwe Schmock

  3. Vienna University of Technology, Wiedner Hauptstrasse, 8-10, A-1040, Vienna, Austria

    Josef Teichmann

Authors
  1. Walter Schachermayer
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  2. Uwe Schmock
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  3. Josef Teichmann
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Corresponding author

Correspondence to Walter Schachermayer .

Editor information

Editors and Affiliations

  1. Laboratoire de Mathématiques, Université de Versailles-St-Quentin, avenue des États-Unis 45, Versailles, 78035, France

    Catherine Donati-Martin

  2. Inst. Recherche, Mathématiques Avancées, Université Strasbourg I, rue René Descartes 7, Strasbourg CX, 67084, France

    Michel Émery

  3. Laboratoire de Mathematiques, Université de Versailles, av. des Etats-Unis 45, Versailles CX, 78035, France

    Alain Rouault

  4. CNRS UMR 6623, Lab. de Mathématiques, Université Besancon, route de Gray 16, Besancon CX, 25030, France

    Christophe Stricker

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© 2009 Springer-Verlag Berlin Heidelberg

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Schachermayer, W., Schmock, U., Teichmann, J. (2009). Non-monotone convergence in the quadratic Wasserstein distance. In: Donati-Martin, C., Émery, M., Rouault, A., Stricker, C. (eds) Séminaire de Probabilités XLII. Lecture Notes in Mathematics(), vol 1979. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01763-6_3

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