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arXiv · 1710.00800

On the entropy power inequality for the Rényi entropy of order [0,1]

Arnaud Marsiglietti·James Melbourne
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Abstract

Using a sharp version of the reverse Young inequality, and a Rényi entropy comparison result due to Fradelizi, Madiman, and Wang, the authors are able to derive Rényi entropy power inequalities for log-concave random vectors when Rényi parameters belong to $(0,1)$. Furthermore, the estimates are shown to be sharp up to absolute constants.

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Arnaud Marsiglietti, James Melbourne. 2018-07-21. On the entropy power inequality for the Rényi entropy of order [0,1]. https://arxiv.org/abs/1710.00800

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