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Using a sharp version of the reverse Young inequality, and a R\'enyi entropycomparison result due to Fradelizi, Madiman, and Wang, the authors are able toderive R\'enyi entropy power inequalities for log-concave random vectors whenR\'enyi parameters belong to $(0,1)$. Furthermore, the estimates are shown tobe sharp up to absolute constants.

On the entropy power inequality for the R\'enyi entropy of order [0,1]