On the Log-Sobolev Constant of Log-Concave Vectors
Functional Analysis
2026-02-17 v3 Metric Geometry
Probability
Abstract
It is well known that if a random vector satisfies a log-Sobolev inequality, all of its marginals have subgaussian tails. In the spirit of the KLS conjecture, we investigate whether this implication can be reversed under a log-concavity assumption. In the general setting, we improve on a result of Bobkov, establishing the best dimension dependent bound on the log-Sobolev constant of subgaussian log-concave measures, and we investigate some special cases.
Keywords
Cite
@article{arxiv.2306.12997,
title = {On the Log-Sobolev Constant of Log-Concave Vectors},
author = {Pierre Bizeul},
journal= {arXiv preprint arXiv:2306.12997},
year = {2026}
}
Comments
Major revision. Minor change of title. Version accepted in Journal of Functional Analysis