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|
|Number of pages||14|
|State||Published - 2013|
|Name||Springer Proceedings in Mathematics and Statistics|
Bibliographical noteFunding 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.
- Convex measures
- Entropy power inequality
- Reverse Brunn-Minkowski inequality
- Rogers-Shephard inequality