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Mathematics > Probability
Title: Sharp local propagation of chaos for mean field particles with $W^{-1,\infty}$ kernels
(Submitted on 19 Mar 2024 (v1), last revised 26 Apr 2024 (this version, v2))
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.
Submission history
From: Songbo Wang [view email][v1] Tue, 19 Mar 2024 21:29:26 GMT (23kb)
[v2] Fri, 26 Apr 2024 13:02:15 GMT (28kb)
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