DocumentCode
3609106
Title
A Strengthened Entropy Power Inequality for Log-Concave Densities
Author
Toscani, Giuseppe
Author_Institution
Dept. of Math., Univ. of Pavia, Pavia, Italy
Volume
61
Issue
12
fYear
2015
Firstpage
6550
Lastpage
6559
Abstract
We show that Shannon´s entropy-power inequality admits a strengthened version in the case in which the densities are log-concave. In such a case, in fact, one can extend the Blachman-Stam argument to obtain a sharp inequality for the second derivative of Shannon´s entropy functional with respect to the heat semigroup.
Keywords
entropy; Blachman-Stam argument; Shannon entropy functional; heat semigroup; log-concave densities; strengthened entropy power inequality; Convex functions; Covariance matrices; Entropy; Heating; Mathematical model; Random variables; Yttrium; Entropy; Stam’s Fisher information inequality; Stam???s Fisher information inequality; entropy-power inequality; information measure; information theory;
fLanguage
English
Journal_Title
Information Theory, IEEE Transactions on
Publisher
ieee
ISSN
0018-9448
Type
jour
DOI
10.1109/TIT.2015.2495302
Filename
7308055
Link To Document