Renyi Entropy Power Inequalities via Normal Transport and Rotation

被引：15
|
作者：
Rioul, Olivier [1 ,2 ]
机构：
[1] Univ Paris Saclay, Telecom ParisTech, LTCI, F-75013 Paris, France
[2] Univ Paris Saclay, Ecole Polytech, F-91128 Palaiseau, France
来源：
ENTROPY | 2018年 / 20卷 / 09期
关键词：
Renyi entropy; entropy power inequalities; transportation arguments; normal distributions; escort distributions; log-concave distributions;
D O I：
10.3390/e20090641
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
Following a recent proof of Shannon's entropy power inequality (EPI), a comprehensive framework for deriving various EPIs for the Renyi entropy is presented that uses transport arguments from normal densities and a change of variable by rotation. Simple arguments are given to recover the previously known Renyi EPIs and derive new ones, by unifying a multiplicative form with constant c and a modification with exponent alpha of previous works. In particular, for log-concave densities, we obtain a simple transportation proof of a sharp varentropy bound.
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收藏
页数：17
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