A note on Talagrand's transportation inequality and logarithmic Sobolev inequality

• 成果类型: Article
• 署名作者: Cattiaux, Patrick; Guillin, Arnaud; Wu, Li-Ming
• 署名单位: Universite Federale Toulouse Midi-Pyrenees (ComUE); Universite de Toulouse; Institut National des Sciences Appliquees de Toulouse; Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Clermont Auvergne (UCA)
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-009-0231-9
• 发表日期: 2010
• 页码: 285-304
• 关键词: information inequalities; cost; CONVERGENCE

摘要

We give by simple arguments sufficient conditions, so called Lyapunov conditions, for Talagrand's transportation information inequality and for the logarithmic Sobolev inequality. Those sufficient conditions work even in the case where the Bakry-Emery curvature is not lower bounded. Several new examples are provided.