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November 2009 A characterization of dimension free concentration in terms of transportation inequalities
Nathael Gozlan
Ann. Probab. 37(6): 2480-2498 (November 2009). DOI: 10.1214/09-AOP470

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.

Citation

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Nathael Gozlan. "A characterization of dimension free concentration in terms of transportation inequalities." Ann. Probab. 37 (6) 2480 - 2498, November 2009. https://doi.org/10.1214/09-AOP470

Information

Published: November 2009
First available in Project Euclid: 16 November 2009

zbMATH: 1201.60016
MathSciNet: MR2573565
Digital Object Identifier: 10.1214/09-AOP470

Subjects:
Primary: 26D10, 60E15, 60F10

Rights: Copyright © 2009 Institute of Mathematical Statistics

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Vol.37 • No. 6 • November 2009
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