On the problem of reversibility of the entropy power inequality

Sergey G. Bobkov; Mokshay M. Madiman

doi:10.1007/978-3-642-36068-8_4

On the problem of reversibility of the entropy power inequality

Sergey G. Bobkov, Mokshay M. Madiman

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

27 Scopus citations

Abstract

As was shown recently by the authors, the entropy power inequality can be reversed for independent summands with sufficiently concave densities, when the distributions of the summands are put in a special position. In this note it is proved that reversibility is impossible over the whole class of convex probability distributions. Related phenomena for identically distributed summands are also discussed.

Original language	English (US)
Title of host publication	Limit Theorems in Probability, Statistics and Number Theory
Subtitle of host publication	In Honor of Friedrich Gotze
Publisher	Springer New York LLC
Pages	61-74
Number of pages	14
ISBN (Print)	9783642360671
DOIs	https://doi.org/10.1007/978-3-642-36068-8_4
State	Published - 2013

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	42
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Bibliographical note

Funding Information:
Sergey G. Bobkov was supported in part by the NSF grant DMS-1106530. Mokshay M. Madiman was supported in part by the NSF CAREER grant DMS-1056996.

Keywords

Convex measures
Entropy power inequality
Log-concave
Reverse Brunn-Minkowski inequality
Rogers-Shephard inequality

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On the problem of reversibility of the entropy power inequality. / Bobkov, Sergey G.; Madiman, Mokshay M.
Limit Theorems in Probability, Statistics and Number Theory: In Honor of Friedrich Gotze. Springer New York LLC, 2013. p. 61-74 (Springer Proceedings in Mathematics and Statistics; Vol. 42).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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On the problem of reversibility of the entropy power inequality

Abstract

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Keywords

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