## Nicolas Gast [1]

Mean field approximation is a widely used technique to study stochastic systems composed of many interacting objects with applications from theoretical physics to biological models and artificial intelligence. The fundamental idea of mean field approximation is the behavior of a large stochastic system os often simpler than the one of a moderate size system because of the law of large number. In this talk, I will introduce the key concepts behind mean field approximation, by giving some examples of where it has been applied. I will review some of the classical models. I will try to answer a very natural question: how large should the system be for mean-field to apply? This leads to a follow-up question: how to refine this approximation to make it applicable for small to moderate size systems?