A DISCRETE COMPLEMENT OF LYAPUNOV'S INEQUALITY AND ITS INFORMATION THEORETIC CONSEQUENCES

• 成果类型: Article
• 署名作者: Elbourne, James m; Palafox -castillo, Gerardo
• 署名单位: Universidad Autonoma de Nuevo Leon
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/22-AAP1919
• 发表日期: 2023
• 页码: 4322-4340
• 关键词: entropy power inequalities; brunn-minkowski inequality; log-concave; variants; volumes; sums

摘要

We establish a reversal of Lyapunov's inequality for monotone logconcave sequences, settling a conjecture of Havrilla-Tkocz and Melbourne- Tkocz. A strengthened version of the same conjecture is disproved through counter example. We also derive several information theoretic inequalities as consequences. In particular sharp bounds are derived for the varentropy, Renyi entropies, and the concentration of information of monotone logconcave random variables. Moreover, the majorization approach utilized in the proof of the main theorem, is applied to derive analogous information theoretic results in the symmetric setting, where the Lyapunov reversal is known to fail.