A characterization of dimension free concentration in terms of transportation inequalities

A characterization of dimension free concentration in terms of transportation inequalities

Nathael Gozlan

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

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.

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Primary Subjects: 60E15, 60F10, 26D10

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

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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

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