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1996 Transportation Approach to Some Concentration Inequalities in Product Spaces
Amir Dembo, Ofer Zeitouni
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Electron. Commun. Probab. 1: 83-90 (1996). DOI: 10.1214/ECP.v1-979

Abstract

Using a transportation approach we prove that for every probability measures $P,Q_1,Q_2$ on $\Omega^N$ with $P$ a product measure there exist r.c.p.d. $\nu_j$ such that $\int \nu_j (\cdot|x) dP(x) = Q_j(\cdot)$ and $$ \int dP (x) \int \frac{dP}{dQ_1} (y)^\beta \frac{dP}{dQ_2} (z)^\beta (1+\beta (1-2\beta))^{f_N(x,y,z)} d\nu_1 (y|x) d\nu_2 (z|x) \le 1 \;, $$ for every $\beta \in (0,1/2)$. Here $f_N$ counts the number of coordinates $k$ for which $x_k \neq y_k$ and $x_k \neq z_k$. In case $Q_1=Q_2$ one may take $\nu_1=\nu_2$. In the special case of $Q_j(\cdot)=P(\cdot|A)$ we recover some of Talagrand's sharper concentration inequalities in product spaces.

Citation

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Amir Dembo. Ofer Zeitouni. "Transportation Approach to Some Concentration Inequalities in Product Spaces." Electron. Commun. Probab. 1 83 - 90, 1996. https://doi.org/10.1214/ECP.v1-979

Information

Accepted: 24 October 1996; Published: 1996
First available in Project Euclid: 25 January 2016

zbMATH: 0916.28003
MathSciNet: MR1423908
Digital Object Identifier: 10.1214/ECP.v1-979

Subjects:
Primary: 60E15
Secondary: 28A35

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