Optimal coupling for mean field limits

TL;DR

This paper reviews recent advances in using optimal coupling methods to quantitatively approximate mean field diffusion equations with large interacting particle systems, highlighting broader models, convergence precision, and long-term behavior insights.

Contribution

It provides a comprehensive review of recent optimal coupling techniques applied to mean field limits, extending their applicability and precision.

Findings

Broader range of models analyzed

More precise convergence measures established

Connections with long-term system behavior explored

Abstract

We review recent quantitative results on the approximation of mean field diffusion equations by large systems of interacting particles, obtained by optimal coupling methods. These results concern a larger range of models, more precise senses of convergence and links with the long time behaviour of the systems to be considered.