# Weak and strong mean-field limits for stochastic Cucker-Smale particle systems

## TL;DR

This paper studies the behavior of particle systems with mean-field interactions and noise, establishing weak and strong convergence results and propagation of chaos, especially for models related to collective motion like Cucker-Smale.

## Contribution

It introduces new weak and strong mean-field limit results for stochastic particle systems with locally Lipschitz kernels, including models of collective motion.

## Key findings

- Constructed weak solutions to the limiting SPDE.
- Established strong L^p convergence under bounded diffusion.
- Proved propagation of chaos for the particle system.

## Abstract

We consider a particle system with a mean-field-type interaction perturbed by some common and individual noises. When the interacting kernels are sublinear and only locally Lipschitz-continuous, relying on arguments based on the tightness of random measures in Wasserstein spaces, we are able to construct a weak solution of the corresponding limiting SPDE. In a setup where the diffusion coefficient on the environmental noise is bounded, this weak convergence can be turned into a strong L^p($\Omega$) convergence and the propagation of chaos for the particle system can be established. The systems considered include perturbations of the Cucker-Smale model for collective motion.