• Corpus ID: 244117205

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

@article{Melbourne2021ADC,
  title={A discrete complement of Lyapunov's inequality and its information theoretic consequences},
  author={James Melbourne and Gerardo Palafox-Castillo},
  journal={ArXiv},
  year={2021},
  volume={abs/2111.06997}
}
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, Rényi entropies, and the concentration of information of monotone logconcave random variables. Moreover, the majorization approach… 

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