Reversal of Renyi Entropy Inequalities Under Log-Concavity

被引：10
|
作者：
Melbourne, James [1 ]
Tkocz, Tomasz [2 ]
机构：
[1] Univ Minnesota, Dept Elect & Comp Engn, Minneapolis, MN 55455 USA
[2] Carnegie Mellon Univ, Dept Math, Pittsburgh, PA 15289 USA
来源：
IEEE TRANSACTIONS ON INFORMATION THEORY | 2021年 / 67卷 / 01期
关键词：
Renyi entropy; entropy power inequality; reversals; log-concave variables; Rogers-Shephard; convex geometry; MAXIMUM-ENTROPY; PROPERTY;
D O I：
10.1109/TIT.2020.3024025
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
We establish a discrete analog of the Renyi entropy comparison due to Bobkov and Madiman. For log-concave variables on the integers, the min entropy is within log epsilon of the usual Shannon entropy. Additionally we investigate the entropic Rogers-Shephard inequality studied by Madiman and Kontoyannis, and establish a sharp Renyi version for certain parameters in both the continuous and discrete cases.
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页码：45 / 51
页数：7
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