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 
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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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2005_328_a13/}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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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[4] V. N. Sudakov, B. S. Tsirelson, “Ekstremalnye svoistva poluprostranstv dlya sfericheski invariantnykh mer”, Zapiski nauchn. semin. LOMI, 41, 1974, 14–24 | MR | Zbl

[5] B. S. Cirel'son, I. A. Ibragimov, V. N. Sudakov, “Norms of Gaussian sample functions”, Lecture Notes in Mathematics, 550, Springer, Berlin, 1976, 20–41 | MR