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
SN - 0012-7094
VL - 119
SP - 41
EP - 63
JO - Duke Mathematical Journal
JF - Duke Mathematical Journal
IS - 1
ER -