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Non-monotone convergence in the quadratic Wasserstein distance

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

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.

    MathSciNet  MATH  Google Scholar 

  2. L. Bachelier, Théorie de la Spéculation, Annales scientifiques de l'Écöle Normale Supérieure Série 3, 17, 1900, pp. 21–86. Also available from the site http://www.numdam.org/

    MathSciNet  MATH  Google Scholar 

  3. W. Schachermayer, Introduction to the Mathematics of Financial Markets, LNM 1816 - Lectures on Probability Theory and Statistics, Saint-Flour summer school 2000 (Pierre Bernard, editor), Springer-Verlag, Heidelberg, 2003, pp. 111–177.

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  4. H. Tanaka, An inequality for a functional of probability distributions and its applications to Kac's one-dimensional model of a Maxwell gas, Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete 27, 1973, pp. 47–52.

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  5. C. Villani, Topics in Optimal Transportation, Graduate Studies in Mathematics 58, American Mathematical Society, Providence Rhode Island, 2003.

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Correspondence to Walter Schachermayer .

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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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