A CHARACTERIZATION OF DIMENSION FREE CONCENTRATION IN TERMS OF TRANSPORTATION INEQUALITIES

• 成果类型: Article
• 署名作者: Gozlan, Nathael
• 署名单位: Universite Gustave-Eiffel; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/09-AOP470
• 发表日期: 2009
• 页码: 2480-2498
• 关键词: logarithmic sobolev inequalities; information inequalities; cost; hypercontractivity

摘要

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 Poincare inequality is equivalent to a certain form of dimension free exponential concentration. The proofs of all these results rely on simple Large Deviations techniques.