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.
Publié le : 2009-11-15
Classification:
Concentration of measure,
transportation-cost inequalities,
Sanov’s theorem,
logarithmic-Sobolev inequalities,
60E15,
60F10,
26D10
@article{1258380796,
author = {Gozlan, Nathael},
title = {A characterization of dimension free concentration in terms of transportation inequalities},
journal = {Ann. Probab.},
volume = {37},
number = {1},
year = {2009},
pages = { 2480-2498},
language = {en},
url = {http://dml.mathdoc.fr/item/1258380796}
}
Gozlan, Nathael. A characterization of dimension free concentration in terms of transportation inequalities. Ann. Probab., Tome 37 (2009) no. 1, pp. 2480-2498. http://gdmltest.u-ga.fr/item/1258380796/