A discrete complement of lyapunov's inequality and its information theoretic consequences
ANNALS OF APPLIED PROBABILITY(2023)
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.
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关键词
Log-concave sequences,reverse Lyapunov,concentration of information,Renyi entropy
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