Functional Inequalities via Lyapunov conditions

TL;DR

This paper reviews recent advances in establishing functional inequalities such as Poincaré, transportation-information, and logarithmic Sobolev inequalities using Lyapunov conditions, offering a simple and effective technique.

Contribution

It introduces a straightforward Lyapunov-based method to derive various functional inequalities, enhancing the toolkit for analysis in probability and analysis.

Findings

Unified Lyapunov approach simplifies proving inequalities.

New results on weak and super Poincaré inequalities.

Effective technique applicable to multiple functional inequalities.

Abstract

We review here some recent results by the authors, and various coauthors, on (weak,super) Poincar\'e inequalities, transportation-information inequalities or logarithmic Sobolev inequality via a quite simple and efficient technique: Lyapunov conditions.