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

Michel Bonnefont, Aldéric Joulin

Published 2023-02-10Version 1

Motivated by some statistical issues derived from Global Sensitivity Analysis, we provide explicit lower bounds with respect to some quantities of interest (parameters of the underlying distribution, dimension, geometrical characteristics of the domain, etc.) on the spectral gap of log-concave probability measures on convex bodies. Our results are illustrated by some classical and less classical examples.