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On the entropy power inequality for the Rényi entropy of order [0,1] (1710.00800v3)
Published 2 Oct 2017 in cs.IT, math.IT, and math.PR
Abstract: Using a sharp version of the reverse Young inequality, and a R\'enyi entropy comparison result due to Fradelizi, Madiman, and Wang, the authors are able to derive R\'enyi entropy power inequalities for log-concave random vectors when R\'enyi parameters belong to $(0,1)$. Furthermore, the estimates are shown to be sharp up to absolute constants.