Modified logarithmic Sobolev inequalities and transportation inequalities

• 成果类型: Article
• 署名作者: Gentil, I; Guillin, A; Miclo, L
• 署名单位: Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS)
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-005-0432-9
• 发表日期: 2005
• 页码: 409-436
• 关键词: convexity; cost

摘要

We present a class of modified logarithmic Sobolev inequality, interpolating between Poincare and logarithmic Sobolev inequalities, suitable for measures of the type exp(-| x|(alpha)) or exp(-| x|(alpha) log(beta) ( 2 + | x|)) (alpha is an element of] 1, 2[ and beta is an element of R) which lead to new concentration inequalities. These modified inequalities share common properties with usual logarithmic Sobolev inequalities, as tensorisation or perturbation, and imply as well Poincare inequality. We also study the link between these new modified logarithmic Sobolev inequalities and transportation inequalities.