On the Entropy Power Inequality for the Rényi Entropy of Order [0, 1]

Using a sharp version of the reverse Young inequality, and a Rényi entropy comparison result due to Fradelizi, Madiman, and Wang (2016), the authors 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.