A NEW CHARACTERIZATION OF TALAGRAND'S TRANSPORT-ENTROPY INEQUALITIES AND APPLICATIONS

• 成果类型: Article
• 署名作者: Gozlan, Nathael; Roberto, Cyril; Samson, Paul-Marie
• 署名单位: Universite Gustave-Eiffel; Universite Paris-Est-Creteil-Val-de-Marne (UPEC)
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/10-AOP570
• 发表日期: 2011
• 页码: 857-880
• 关键词: logarithmic sobolev inequalities; gradient flows; SPACES; cost

摘要

We show that Talaurand's transport inequality is equivalent to a restricted logarithmic Sobolev inequality. This result clarifies the links between these two important functional inequalities. As an application, we give the first proof of the fact that Talagrand's inequality is stable under bounded perturbations.