A Generalization of the Concavity of Renyi Entropy Power

doi:10.3390/e23121593

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	A Generalization of the Concavity of Renyi Entropy Power
	Guo, Laigang 1; Yuan, Chun-Ming 2,3; Gao, Xiao-Shan 2,3
	2021-12-01
发表期刊	ENTROPY
卷号	23 期号:12 页码:18
摘要	Recently, Savare-Toscani proved that the Renyi entropy power of general probability densities solving the p-nonlinear heat equation in R n is a concave function of time under certain conditions of three parameters n , p , mu , which extends Costa's concavity inequality for Shannon's entropy power to the Renyi entropy power. In this paper, we give a condition f ( n , p , mu ) of n , p , mu under which the concavity of the Renyi entropy power is valid. The condition f ( n , p , mu ) contains Savare-Toscani's condition as a special case and much more cases. Precisely, the points ( n , p , mu ) satisfying Savare-Toscani's condition consist of a two-dimensional subset of R (3) , and the points satisfying the condition f ( n , p , mu ) consist a three-dimensional subset of R (3) . Furthermore, f ( n , p , mu ) gives the necessary and sufficient condition in a certain sense. Finally, the conditions are obtained with a systematic approach.
关键词	Renyi entropy entropy power inequality nonlinear heat equation
DOI	10.3390/e23121593
收录类别	SCI
语种	英语
资助项目	NSFC[11688101] ; NSFC[NKRDP 2018YFA0704705] ; Beijing Natural Science Foundation[Z190004] ; Fundamental Research Funds for the Central Universities[2021NTST32]
WOS研究方向	Physics
WOS类目	Physics, Multidisciplinary
WOS记录号	WOS:000738892800001
出版者	MDPI
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/59851
专题	中国科学院数学与系统科学研究院
通讯作者	Gao, Xiao-Shan
作者单位	1.Beijing Normal Univ, Sch Math Sci, Lab Math & Complex Syst, Minist Educ, Beijing 100875, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, KLMM, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Guo, Laigang,Yuan, Chun-Ming,Gao, Xiao-Shan. A Generalization of the Concavity of Renyi Entropy Power[J]. ENTROPY,2021,23(12):18.
APA	Guo, Laigang,Yuan, Chun-Ming,&Gao, Xiao-Shan.(2021).A Generalization of the Concavity of Renyi Entropy Power.ENTROPY,23(12),18.
MLA	Guo, Laigang,et al."A Generalization of the Concavity of Renyi Entropy Power".ENTROPY 23.12(2021):18.