Rényi entropy power inequality and a reverse
Volume 242 / 2018
Studia Mathematica 242 (2018), 303-319
MSC: Primary 94A17; Secondary 62B10, 52Axx.
DOI: 10.4064/sm170521-5-8
Published online: 16 February 2018
Abstract
The aim of this paper is twofold. In the first part, we present a refinement of the Rényi Entropy Power Inequality (EPI) recently obtained by Bobkov and Marsiglietti (2016). The proof largely follows the approach of Dembo et al. (1991) of employing Young’s convolution inequalities with sharp constants. In the second part, we study the reversibility of the Rényi EPI, and confirm a conjecture of Ball et al. (2016) and Madiman et al. (2016) in two cases. Connections with various $p$th mean bodies in convex geometry are also explored.
