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

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.