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

Songbo Wang

doi:10.1016/j.jfa.2025.111240

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arXiv · 2403.13161

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

Songbo Wang

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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.

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Songbo Wang. 2024-03-19. Sharp local propagation of chaos for mean field particles with $W^{-1,\infty}$ kernels. https://doi.org/10.1016/j.jfa.2025.111240

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