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
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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.
@article{ZNSL_2005_328_a13,
author = {V. N. Sudakov},
title = {Gaussian concentration in the {Kantorovich} metric of distributions of random variables and the quantile functions},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {230--235},
publisher = {mathdoc},
volume = {328},
year = {2005},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2005_328_a13/}
}
TY - JOUR AU - V. N. Sudakov TI - Gaussian concentration in the Kantorovich metric of distributions of random variables and the quantile functions JO - Zapiski Nauchnykh Seminarov POMI PY - 2005 SP - 230 EP - 235 VL - 328 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZNSL_2005_328_a13/ LA - ru ID - ZNSL_2005_328_a13 ER -
%0 Journal Article %A V. N. Sudakov %T Gaussian concentration in the Kantorovich metric of distributions of random variables and the quantile functions %J Zapiski Nauchnykh Seminarov POMI %D 2005 %P 230-235 %V 328 %I mathdoc %U http://geodesic.mathdoc.fr/item/ZNSL_2005_328_a13/ %G ru %F ZNSL_2005_328_a13
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/