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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)
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
MDPI and ACS Style

Rioul, O. Rényi Entropy Power Inequalities via Normal Transport and Rotation. Entropy 2018, 20, 641.

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