Hypercontractive Measures, Talagrand’s Inequality, and Influences

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• 作者：Dario Cordero-Erausquin (1) (2)
  Michel Ledoux (2) (3)
  
• 刊名：Lecture Notes in Mathematics
• 出版年：2012
• 出版时间：2012
• 年：2012
• 卷：2050
• 期：1
• 页码：191-204
• 全文大小：251KB
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• 作者单位：Dario Cordero-Erausquin (1) (2)
  Michel Ledoux (2) (3)
  
  1. Institut de Mathématiques, Université Pierre et Marie Curie (Paris 6 -Jussieu), 4 place Jussieu, 75005, Paris, France
  2. Institut Universitaire de France, Paris, France
  3. Institut de Mathématiques de Toulouse, Université de Toulouse, 31062, Toulouse, France
  

文摘

We survey several Talagrand type inequalities and their application to influences with the tool of hypercontractivity for both discrete and continuous, and product and non-product models. The approach covers similarly by a simple interpolation the framework of geometric influences recently developed by N. Keller, E. Mossel and A. Sen. Geometric Brascamp-Lieb decompositions are also considered in this context.