A note on the spectral gap for log-concave probability measures on convex bodies

2023/02/10 by Michel Bonnefont, Bonnefont, Michel, Aldéric Joulin +1
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Markov Chains and Monte Carlo Methods #Point processes and geometric inequalities #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2302.05207

openalex publication_date 2023/02/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

In this paper, we provide explicit lower bounds with respect to some quantities of interest (parameters of the underlying distribution, dimension, geometrical characteristics of the domain, position of the origin, etc.) on the spectral gap of log-concave probability measures on convex bodies. Our results are illustrated by some classical and less classical examples.

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