The Annals of Probability

A characterization of dimension free concentration in terms of transportation inequalities

Nathael Gozlan

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Abstract

The aim of this paper is to give a characterization of the dimension free concentration of measure phenomenon in terms of transportation-cost inequalities. We apply this theorem to give a new and very short proof of a result by Otto and Villani. Another application is to show that the Poincaré inequality is equivalent to a certain form of dimension free exponential concentration. The proofs of all these results rely on simple Large Deviations techniques.

Article information

Source
Ann. Probab. Volume 37, Number 6 (2009), 2480-2498.

Dates
First available in Project Euclid: 16 November 2009

Permanent link to this document
http://projecteuclid.org/euclid.aop/1258380796

Digital Object Identifier
doi:10.1214/09-AOP470

Mathematical Reviews number (MathSciNet)
MR2573565

Zentralblatt MATH identifier
05708808

Subjects
Primary: 60E15: Inequalities; stochastic orderings 60F10: Large deviations 26D10: Inequalities involving derivatives and differential and integral operators

Keywords
Concentration of measure transportation-cost inequalities Sanov’s theorem logarithmic-Sobolev inequalities

Citation

Gozlan, Nathael. A characterization of dimension free concentration in terms of transportation inequalities. The Annals of Probability 37 (2009), no. 6, 2480--2498. doi:10.1214/09-AOP470. http://projecteuclid.org/euclid.aop/1258380796.


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