Entropy jumps in the presence of a spectral gap

Keith Ball, Franck Barthe, Assf Naor

Research output: Contribution to journalArticle

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

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Entropy jumps in the presence of a spectral gap. / Ball, Keith; Barthe, Franck; Naor, Assf.

In: Duke Mathematical Journal, Vol. 119, No. 1, 15.07.2003, p. 41-63.

Research output: Contribution to journalArticle

Ball, Keith ; Barthe, Franck ; Naor, Assf. / Entropy jumps in the presence of a spectral gap. In: Duke Mathematical Journal. 2003 ; Vol. 119, No. 1. pp. 41-63.
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