Stochastic mean-field limit: non-Lipschitz forces and swarming (Q2883363)

The authors consider general stochastic systems of interacting particles with noise which are relevant as models for the collective behavior of animals, and rigorously prove that in the mean-field limit the system is close to the solution of a kinetic PDE. The main purpose is to include models widely studied in the literature such as the Cucker-Smale model, adding noise to the behavior of individuals. The difficulty, as compared to the classical case of globally Lipschitz potentials, is that in several models the interaction potential between particles is only locally Lipschitz, the local Lipschitz constant growing to infinity with the size of the region considered. With this in mind, they present an extension of the classical theory for globally Lipschitz interactions, which works for only locally Lipschitz ones. This work is interesting. The paper is novel, clear and concise. It is deserved to be read.