Geodesic
Gaussian concentration in the Kantorovich metric of distributions of random variables and the quantile functions
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 9, Tome 328 (2005), pp. 230-235 Cet article a éte moissonné depuis la source Math-Net.Ru

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A sketch of the proof of the following theorem. Let the unit ball of the kernel space $H_\gamma$ of a centered Gaussian measure $\gamma$ in the space $L^2$ is a subspace of the unit ball of this space. There exists a (“typical”) univariate distribution $\bar{\mathbf P}_\gamma$ such that the expectation with respect to $\gamma$ of the Kantorovich distance between the distribution of an element of $L^2$ chosen at random and this typical distribution is less than 0.8. 
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V. N. Sudakov. Gaussian concentration in the Kantorovich metric of distributions of random variables and the quantile functions. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 9, Tome 328 (2005), pp. 230-235. http://geodesic.mathdoc.fr/item/ZNSL_2005_328_a13/

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