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The transportation cost for the cube

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1745)

Abstract

The transportation method for proving concentration of measure results works directly for the cube. Here we find the best constant that can be found using this method which turns out to be better than those obtained by previous methods and which cannot be far from that which is best possible.

Keywords

  • Transportation Cost
  • Product Space
  • Good Constant
  • Logarithmic Sobolev Inequality
  • Informational Divergence

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Supported by EPSRC-97409672.

This work will form part of a Ph.D. thesis which is being supervised by Keith Ball.

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References

  1. Bttazzo G., Giaquinta M., Hildebrandt S. (1998) One-Dimensional Variational Problems. Oxford Lecture Series in Mathematics and its Applications, 15, Clarendon Press, Oxford

    Google Scholar 

  2. Marton K. (1996) Bounding \(\bar d\)-distance by informational divergence: a method to prove measure concentration. The Annals of Probability 24(2):857–866

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. Otto F., Villani C. (1999) Generalization of an inequality by Talagrand, and links with the logarithmic Sobolev inequality. Preprint

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  4. Talagrand M. (1996) Transportation cost for Gaussian and other product measures. Geometric and Functional Analysis 6(3):587–599

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. Tsirel'son B.S., Ibragimov I.A., Sudakov V.N. (1976) Norms of Gaussian sample functions. Proceedings of the Third Japan-USSR Symposium on Probability Theory, Lecture Notes in Mathematics, 550

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© 2000 Springer-Verlag

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Anttila, M. (2000). The transportation cost for the cube. In: Milman, V.D., Schechtman, G. (eds) Geometric Aspects of Functional Analysis. Lecture Notes in Mathematics, vol 1745. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0107202

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  • DOI: https://doi.org/10.1007/BFb0107202

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41070-6

  • Online ISBN: 978-3-540-45392-5

  • eBook Packages: Springer Book Archive