From Brunn-Minkowski to Brascamp-Lieb and to logarithmic Sobolev inequalities

S. G. Bobkov, M. Ledoux

Research output: Contribution to journalArticle

100 Scopus citations

Abstract

We develop several applications of the Brunn-Minkowski inequality in the Prékopa-Leindler form. In particular, we show that an argument of B. Maurey may be adapted to deduce from the Prékopa-Leindler theorem the Brascamp-Lieb inequality for strictly convex potentials. We deduce similarly the logarithmic Sobolev inequality for uniformly convex potentials for which we deal more generally with arbitrary norms and obtain some new results in this context. Applications to transportation cost and to concentration on uniformly convex bodies complete the exposition.

Original languageEnglish (US)
Pages (from-to)1028-1052
Number of pages25
JournalGeometric and Functional Analysis
Volume10
Issue number5
DOIs
StatePublished - Jan 1 2000

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