Propagation of chaos: a review of models, methods and applications. I. Models and methods

TL;DR

This review discusses the concept of propagation of chaos in large interacting particle systems, covering models, methods, and applications across statistical physics and applied mathematics.

Contribution

It provides a comprehensive overview of classical and recent models and methods related to propagation of chaos, including detailed applications and model analyses.

Findings

Overview of McKean-Vlasov diffusion models

Analysis of mean-field jump models

Discussion of Boltzmann models and their applications

Abstract

The notion of propagation of chaos for large systems of interacting particles originates in statistical physics and has recently become a central notion in many areas of applied mathematics. The present review describes old and new methods as well as several important results in the field. The models considered include the McKean-Vlasov diffusion, the mean-field jump models and the Boltzmann models. The first part of this review is an introduction to modelling aspects of stochastic particle systems and to the notion of propagation of chaos. The second part presents concrete applications and a more detailed study of some of the important models in the field.