Quantitative particle approximation of nonlinear Fokker-Planck equations with singular kernel

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In this work, we study the convergence of the empirical measure of moderately interacting particle systems with singular interaction kernels.

• First, we prove quantitative convergence of the time marginals of the empirical measure of particle positions towards the solution of the limiting nonlinear Fokker-Planck equation.
• Second, we prove the well-posedness for the McKean-Vlasov SDE involving such singular kernels and the convergence of the empirical measure towards it (propagation of chaos).
• Our results only require very weak regularity on the interaction kernel, including the Biot-Savart kernel, and attractive kernels such as Riesz and Keller-Segel kernels in arbitrary dimension.