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RΓ©nyi entropy power inequality and a reverse
April 09, 2017 Β· Declared Dead Β· π arXiv.org
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Authors
Jiange Li
arXiv ID
1704.02634
Category
math.PR
Cross-listed
cs.IT,
math.FA
Citations
34
Venue
arXiv.org
Last Checked
6 months ago
Abstract
This paper is twofold. In the first part, we present a refinement of the RΓ©nyi 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 RΓ©nyi EPI, and confirm a conjecture in \cite{BNT15, MMX16} in two cases. Connections with various $p$-th mean bodies in convex geometry are also explored.
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