Sharp local propagation of chaos for mean field particles with W^-1,∞ kernels

2024/03/19 by Songbo Wang, Wang, Songbo · 3 citations
Mathematics · Physics and Astronomy · #Stochastic processes and statistical mechanics #Mathematical Dynamics and Fractals #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2403.13161

Abstract

We present two methods to obtain O(1/N²) local propagation of chaos bounds for N diffusive particles in W^-1,∞ 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 L² 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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