Benedetta Bertoli (Imperial): Stability and phase transitions of mean field particle systems

Interacting particle systems are a key tool for understanding the behaviour of multi-agent dynamics in many different areas, including, for example, mathematical biology, collective dynamics, machine learning and biophysics. In this talk, we will analyse the system of stochastic differential equations describing such models, and its mean field limit. We derive rigorous results about the behaviour of the stationary solutions of the corresponding Fokker-Planck PDEs, and study how these change in relation to the interaction potential. We will also look at how to extend these and other results to the case where the interacting particles lie on a sequence of random graphs.