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arXiv · 2205.04069

Log-concavity and discrete degrees of freedom

Jacek Jakimiuk·Daniel Murawski·Piotr Nayar·Semen Słobodianiuk
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Abstract

We develop the notion of discrete degrees of freedom of a log-concave sequence and use it to prove that geometric distribution minimises Rényi entropy of order infinity under fixed variance, among all discrete log-concave random variables in $\mathbb{Z}$. We also show that the quantity $\mathbb{P}(X=\mathbb{E} X)$ is maximised, among all ultra-log-concave random variables with fixed integral mean, for a Poisson distribution.

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Jacek Jakimiuk, Daniel Murawski, Piotr Nayar, Semen Słobodianiuk. 2023-05-06. Log-concavity and discrete degrees of freedom. https://arxiv.org/abs/2205.04069

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