A note on the Modified Log-Sobolev inequality

TL;DR

This paper introduces a new criterion for the Modified Logarithmic Sobolev inequality applicable to a broader class of measures on metric measure spaces, extending beyond traditional log-concavity assumptions.

Contribution

The paper presents a criterion based on U-bound inequalities that broadens the applicability of the Modified Log-Sobolev inequality to non-log-concave measures.

Findings

Establishes a new criterion for the inequality

Extends applicability beyond log-concave measures

Utilizes U-bound inequalities for proof

Abstract

A criterion is presented for the Modified Logarithmic Sobolev inequality on metric measure spaces. The criterion based on U-bound inequalities introduced by Hebisch and Zegarlinski allows to show the inequality for measures that go beyond log-concavity.