关于r熵的完全单调猜想

arXiv - CS - Information Theory Pub Date : 2023-12-04 DOI:arxiv-2312.01819

Hao Wu, Lei Yu, Laigang Guo

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引用次数: 0

摘要

本文将香农熵的完全单调猜想推广到R\ enyi熵。当R\ enyi熵的阶数在一定范围内时，我们证实了这一猜想。我们还研究了R′enyi熵幂的凹性和Tsallis熵的完全单调猜想。我们观察到，对于2阶的Tsallis熵，完全单调猜想是成立的。本文的证明是基于分部积分和平方和的方法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On the Completely Monotone Conjecture for Rényi Entropy

In this paper, we generalize the completely monotone conjecture from Shannon entropy to the R\'enyi entropy. We confirm this conjecture for the order of derivative up to $3$, when the order of R\'enyi entropy is in certain regimes. We also investigate concavity of R\'enyi entropy power and the completely monotone conjecture for Tsallis entropy. We observe that the completely monotone conjecture is true for Tsallis entropy of order $2$. Our proofs in this paper are based on the techniques of integration-by-parts and sum-of-squares.

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arXiv - CS - Information Theory

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