The Annals of Probability

A characterization of dimension free concentration in terms of transportation inequalities

Nathael Gozlan

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

First available in Project Euclid: 16 November 2009

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

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


Gozlan, Nathael. A characterization of dimension free concentration in terms of transportation inequalities. Ann. Probab. 37 (2009), no. 6, 2480--2498. doi:10.1214/09-AOP470.

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