English

A Generalization of the Concavity of R\'{e}nyi Entropy Powe

Information Theory 2021-12-15 v1 math.IT

Abstract

Recently, Savar\'{e}-Toscani proved that the R\'{e}nyi entropy power of general probability densities solving the pp-nonlinear heat equation in Rn\mathbb{R}^n is always a concave function of time, which extends Costa's concavity inequality for Shannon's entropy power to R\'{e}nyi entropies. In this paper, we give a generalization of Savar\'{e}-Toscani's result by giving a class of sufficient conditions of the parameters under which the concavity of the R\'{e}nyi entropy power is still valid. These conditions are quite general and include the parameter range given by Savar\'{e}-Toscani as special cases. Also, the conditions are obtained with a systematical approach.

Keywords

Cite

@article{arxiv.2103.06650,
  title  = {A Generalization of the Concavity of R\'{e}nyi Entropy Powe},
  author = {Laigang Guo and Chun-Ming Yuan and Xiao-Shan Gao},
  journal= {arXiv preprint arXiv:2103.06650},
  year   = {2021}
}