Rioul, O. Rényi Entropy Power Inequalities via Normal Transport and Rotation. Entropy2018, 20, 641.
Rioul, O. Rényi Entropy Power Inequalities via Normal Transport and Rotation. Entropy 2018, 20, 641.
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.
Rényi entropy; entropy power inequalities; transportation arguments; normal distributions; escort distributions; log-concave distributions
MATHEMATICS & COMPUTER SCIENCE, Probability and Statistics
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.