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.
"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