# Long time behaviour and mean-field limit of Atlas models

## TL;DR

This paper reviews the long-term and large-scale behavior of Atlas models, a type of rank-based diffusion system used in financial modeling, with a focus on mean-field interactions and applications to capital distribution.

## Contribution

It provides a comprehensive review of the long-time and mean-field behavior of Atlas models, highlighting their application to large-agent financial systems.

## Key findings

- Characterization of long-term behavior of Atlas models
- Analysis of mean-field limit in rank-based diffusions
- Application to modeling capital distribution among agents

## Abstract

This article reviews a few basic features of systems of one-dimensional diffusions with rank-based characteristics. Such systems arise in particular in the modelling of financial markets , where they go by the name of Atlas models. We mostly describe their long time and large scale behaviour, and lay a particular emphasis on the case of mean-field interactions. We finally present an application of the reviewed results to the modelling of capital distribution in systems with a large number of agents.