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Open AccessFeature PaperArticle

Rényi Entropy Power Inequalities via Normal Transport and Rotation

1
LTCI, Télécom ParisTech, Université Paris-Saclay, 75013 Paris, France
2
École Polytechnique, Université Paris-Saclay, 91128 Palaiseau, France
Entropy 2018, 20(9), 641; https://doi.org/10.3390/e20090641
Received: 7 July 2018 / Revised: 22 August 2018 / Accepted: 23 August 2018 / Published: 26 August 2018
(This article belongs to the Special Issue Entropy: From Physics to Information Sciences and Geometry)
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PDF [305 KB, uploaded 26 August 2018]

Abstract

Following a recent proof of Shannon’s entropy power inequality (EPI), a comprehensive framework for deriving various EPIs for the Rényi 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 Rényi EPIs and derive new ones, by unifying a multiplicative form with constant c and a modification with exponent α of previous works. In particular, for log-concave densities, we obtain a simple transportation proof of a sharp varentropy bound. View Full-Text
Keywords: Rényi entropy; entropy power inequalities; transportation arguments; normal distributions; escort distributions; log-concave distributions Rényi entropy; entropy power inequalities; transportation arguments; normal distributions; escort distributions; log-concave distributions
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Rioul, O. Rényi Entropy Power Inequalities via Normal Transport and Rotation. Entropy 2018, 20, 641.

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