On the log-Sobolev constant of log-concave measures

2023/06/22 by Bizeul, Pierre
#FOS: Mathematics #Functional Analysis (math.FA) #Metric Geometry (math.MG) #Probability (math.PR)

paper · doi:10.48550/arxiv.2306.12997

Abstract

It is well known that a log-Sobolev inequality implies sub-gaussian decay of the 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.

Related

• Subadditivity of the log-Sobolev constant on convolutions
• Logarithmic Sobolev inequality for log-concave measure from Prekopa-Leindler inequality
• Log-concavity and strong log-concavity: a review
• Modified log-Sobolev inequalities for strongly log-concave distributions
• Elementary proof of logarithmic Sobolev inequalities for Gaussian convolutions on ℝ