Rényi entropy power inequality and a reverse

This paper is twofold. In the first part, we present a refinement of the R\'enyi Entropy Power Inequality (EPI) recently obtained in \cite{BM16}. The proof largely follows the approach in \cite{DCT91} of employing Young's convolution inequalities with sharp constants. In the second part, we study the reversibility of the R\'enyi EPI, and confirm a conjecture in \cite{BNT15, MMX16} in two cases. Connections with various $p$-th mean bodies in convex geometry are also explored.

• Publication year

  2017

• Venue

  arXiv.org

• Publication date

  2017-04-09

• Fields of study

  Mathematics, Computer Science

• Identifiers
  DOI 10.4064/SM170521-5-8arXiv 1704.02634
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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