Stochastic Mean-Field Limit: Non-Lipschitz Forces & Swarming

We 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 solutio n of a kinetic PDE. Our aim is to include models widely studied in the literature such as the CuckerSmale model, adding noise to the behavior of individuals. The difficulty, as compared to the classical case of globally Lipschitz potentials, is t hat in several models the interaction potential between particles is only locally Li pschitz, the local Lipschitz constant growing to infinity with the size of the region consi dered. With this in mind, we present an extension of the classical theory for globally Lipschitz interactions, which works for only locally Lipschitz ones.

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