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 -nonlinear heat equation in 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}
}