Propagation of chaos: a review of models, methods and applications. I. Models and methods
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 McKeanVlasov diffusion, the meanfield 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.
 Publication:

arXiv eprints
 Pub Date:
 February 2022
 DOI:
 10.48550/arXiv.2203.00446
 arXiv:
 arXiv:2203.00446
 Bibcode:
 2022arXiv220300446C
 Keywords:

 Mathematics  Probability;
 Mathematical Physics;
 Mathematics  Analysis of PDEs;
 Mathematics  History and Overview;
 82C22;
 82C40;
 35Q70;
 65C35;
 9210
 EPrint:
 148 pages. This is the first part of a twopart review article. The second part can be accessed at arXiv:2106.14812