Uniform-in-time propagation of chaos for mean field Langevin dynamics

Understand

We study the mean field Langevin dynamics and the associated particle system.

• By assuming the functional convexity of the energy, we obtain the $L^p$-convergence of the marginal distributions towards the unique invariant measure for the mean field dynamics.
• Furthermore, we prove the uniform-in-time propagation of chaos in both the $L^2$-Wasserstein metric and relative entropy.