Abstract
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.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 328, 2005, pp. 230–235.
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Sudakov, V.N. Gaussian concentration in the Kantorovich metric of distributions of random variables and the quantile functions. J Math Sci 139, 6631–6633 (2006). https://doi.org/10.1007/s10958-006-0379-0
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DOI: https://doi.org/10.1007/s10958-006-0379-0