Sharp Local Propagation of Chaos for Mean Field Particles with $W^{-1,\infty}$ Kernels
Time: 2024-03-28
Published By: He Liu
Speaker(s): Songbo Wang(École Polytechnique, France)
Time: 16:00-17:30 April 24, 2024
Venue: Online
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. 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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