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arXiv · 2205.08293

Concentration inequalities for log-concave sequences

Arnaud Marsiglietti·James Melbourne
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Abstract

We investigate quantitative implications of the notion of log-concavity through a probabilistic interpretation. In particular, we derive concentration inequalities, moment and entropy bounds for random variables satisfying a precise degree of log-concavity. Along the way, we recover, improve, and simplify several results existing in the literature. Our approach is based on majorization in the convex order.

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Arnaud Marsiglietti, James Melbourne. 2022-05-17. Concentration inequalities for log-concave sequences. https://arxiv.org/abs/2205.08293

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