R\'enyi entropy power inequality and a reverse
Probability
2018-05-01 v2 Information Theory
Functional Analysis
math.IT
Abstract
This paper is twofold. In the first part, we present a refinement of the R\'enyi Entropy Power Inequality (EPI) recently obtained in \cite{BM16}. The proof largely follows the approach in \cite{DCT91} of employing Young's convolution inequalities with sharp constants. In the second part, we study the reversibility of the R\'enyi EPI, and confirm a conjecture in \cite{BNT15, MMX16} in two cases. Connections with various -th mean bodies in convex geometry are also explored.
Cite
@article{arxiv.1704.02634,
title = {R\'enyi entropy power inequality and a reverse},
author = {Jiange Li},
journal= {arXiv preprint arXiv:1704.02634},
year = {2018}
}