Sharp local propagation of chaos for mean field particles with $W^{-1,\infty }$ kernels

Abstract

We present two methods to obtain $O(1/N^2)$ local propagation of chaos bounds for $N$ diffusive particles in $W^{-1,\infty }$ mean field interaction. This extends the recent finding of Lacker [Probab. Math. Phys., 4(2):377-432, 2023] to the case of singular interactions. The first method is based on a hierarchy of relative entropies and Fisher informations, and applies to the 2D viscous vortex model in the high temperature regime. Time-uniform local chaos bounds are also shown in this case. In the second method, we work on a hierarchy of $L^2$ distances and Dirichlet energies, and derive the desired sharp estimates for the same model in short time without restrictions on the temperature.

34 pages; accepted version

References in corpus (4)

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• A new approach to the mean-field limit of Vlasov-Fokker-Planck equations
• Time-uniform log-Sobolev inequalities and applications to propagation of chaos
• Higher-order propagation of chaos in $L^2$ for interacting diffusions