Concentration inequalities for log-concave sequences

2022/05/17 by Arnaud Marsiglietti, Marsiglietti, Arnaud, James Melbourne +1 · 1 citation
Mathematics · Physics and Astronomy · #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Statistical Mechanics and Entropy #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.2205.08293

openalex publication_date 2022/05/17 · openalex created_date 2022/05/22 · openalex updated_date 2026/07/28

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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• On Convex Functions of Gaussian Variables

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