Entropy jumps in the presence of a spectral gap

Keith Ball, Franck Barthe, Assf Naor

Research output: Contribution to journalArticle

39 Scopus citations

Abstract

It is shown that if X is a random variable whose density satisfies a Poincaré inequality, and Y is an independent copy of X, then the entropy of (X + Y)/2√ is greater than that of X by a fixed fraction of the entropy gap between X and the Gaussian of the same variance. The argument uses a new formula for the Fisher information of a marginal, which can be viewed as a local, reverse form of the Brunn-Minkowski ineauality (in its functional form due to A. Prékopa and L. Leindler).

Original languageEnglish (US)
Pages (from-to)41-63
Number of pages23
JournalDuke Mathematical Journal
Volume119
Issue number1
DOIs
StatePublished - Jul 15 2003
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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