Journal of Mathematical Sciences

, Volume 139, Issue 3, pp 6631–6633 | Cite as

Gaussian concentration in the Kantorovich metric of distributions of random variables and the quantile functions

  • V. N. Sudakov


We give a sketch of the proof of the following theorem. Assume that the unit ball of the kernel space Hγ of a centered Gaussian measure λ in the space L2 is a subspace of the unit ball of this space. Then there exists a (“typical”) univariate distribution \(\bar P_\gamma \) such that the expectation with respect to γ of the Kantorovich distance between the distribution of an element of L2 chosen at random and this typical distribution is less than 0.8. Bibliography: 5 titles.


Unit Ball Sojourn Time Gaussian Measure Quantile Function Sample Function 
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  1. 1.
    V. N. Sudakov, “Gaussian measures. A brief survey,” Rend. Istit. Mat. Univ. Trieste, 26,suppl., 289–325 (1994).MATHMathSciNetGoogle Scholar
  2. 2.
    V. N. Sudakov and A. V. Sudakov, “Dependent Gaussian samples: estimates for the scatter independent of the sample size,” Zap. Nauchn. Semin. POMI, 320, 166–173 (2004).MATHMathSciNetGoogle Scholar
  3. 3.
    A. V. Sudakov, V. N. Sudakov, and H. v. Weizsacker, “Typical distributions: infinite-dimensional approaches,” in: Asymptotic Methods in Probability and Statistics with Applications, Birkhauser, Boston (2001), pp. 205–212.Google Scholar
  4. 4.
    V. N. Sudakov and B. S. Tsirelson, “Extremal properties of half-spaces for spherically invariant measures,” Zap. Nauchn. Semin. LOMI, 41, 14–24 (1974).MATHGoogle Scholar
  5. 5.
    B. S. Cirel’son, I. A. Ibragimov, and V. N. Sudakov, “Norms of Gaussian sample functions,” Lect. Notes Math., 550, 20–41 (1976).MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • V. N. Sudakov
    • 1
  1. 1.St.Petersburg Department of the Steklov Mathematical InstituteSt.PetersburgRussia

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