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

TL;DR

This paper derives explicit lower bounds for the spectral gap of log-concave probability measures on convex bodies, considering various parameters like distribution characteristics, dimension, and geometry, supported by classical and novel examples.

Contribution

It provides new explicit lower bounds on the spectral gap for log-concave measures on convex bodies, linking geometric and distributional parameters.

Findings

Explicit lower bounds depend on distribution and geometric parameters

Results apply to classical and less classical convex bodies

Spectral gap estimates improve understanding of measure concentration

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.