Mean-Field Coupled Systems and Self-Consistent Transfer Operators: A Review

TL;DR

This review surveys the development of mean-field coupled maps, highlighting recent ergodic theory results on thermodynamic limits and self-consistent transfer operators, and discusses related continuous-time systems and applications.

Contribution

It provides a comprehensive overview of mean-field coupled maps, emphasizing recent theoretical advances and connecting to related fields and practical applications.

Findings

Recent ergodic theory results on thermodynamic limits

Analysis of self-consistent transfer operators

Connections to continuous-time mean-field systems

Abstract

In this review we survey the literature on mean-field coupled maps. We start with the early works from the physics literature, arriving to some recent results from ergodic theory studying the thermodynamic limit of globally coupled maps and the associated self-consistent transfer operators. We also give few pointers to related research fields dealing with mean-field coupled systems in continuous time, and applications.