TY - JOUR

T1 - Entropy jumps in the presence of a spectral gap

AU - Ball, Keith

AU - Barthe, Franck

AU - Naor, Assf

N1 - Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.

PY - 2003/7/15

Y1 - 2003/7/15

N2 - 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).

AB - 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).

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U2 - 10.1215/S0012-7094-03-11912-2

DO - 10.1215/S0012-7094-03-11912-2

M3 - Article

AN - SCOPUS:0042236601

VL - 119

SP - 41

EP - 63

JO - Duke Mathematical Journal

JF - Duke Mathematical Journal

SN - 0012-7094

IS - 1

ER -