Gaussian concentration in the Kantorovich metric of distributions of random variables and the quantile functions
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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.
KeywordsUnit Ball Sojourn Time Gaussian Measure Quantile Function Sample Function
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- 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