English

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 pp-th mean bodies in convex geometry are also explored.

Keywords

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}
}
R2 v1 2026-06-22T19:12:13.537Z