A discrete complement of Lyapunov's inequality and its information theoretic consequences

Autor:	Melbourne, James, Palafox-Castillo, Gerardo
Rok vydání:	2021
Předmět:	Computer Science - Information Theory Mathematics - Functional Analysis Mathematics - Probability
Druh dokumentu:	Working Paper
Popis:	We establish a reversal of Lyapunov's inequality for monotone log-concave 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, R\'enyi entropies, and the concentration of information of monotone log-concave 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. Comment: 16 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2111.06997 Zobrazit plný text záznamu View this record from Arxiv