On the problem of reversibility of the entropy power inequality

Sergey G. Bobkov, Mokshay M. Madiman

Research output: Chapter in Book/Report/Conference proceedingConference contribution

20 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 languageEnglish (US)
Title of host publicationLimit Theorems in Probability, Statistics and Number Theory
Subtitle of host publicationIn Honor of Friedrich Gotze
PublisherSpringer New York LLC
Pages61-74
Number of pages14
ISBN (Print)9783642360671
DOIs
StatePublished - 2013

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume42
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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