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.
Bibliographical noteFunding Information:
Manuscript received November 10, 2017; revised July 20, 2018; accepted October 7, 2018. Date of publication October 23, 2018; date of current version February 14, 2019. A. Marsiglietti was supported by the Walter S. Baer and Jeri Weiss CMI Postdoctoral Fellowship. J. Melbourne was supported by NSF under Grant CNS 1544721 and Grant ECCS 1809194. This paper was presented at the 2018 IEEE International Symposium on Information Theory.
- Entropy power inequality
- Rényi entropy