Sharp local propagation of chaos for mean field particles with $W^{-1,\infty}$ kernels
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914128411492352 |
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| author | Wang, Songbo |
| author_facet | Wang, Songbo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_13161 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sharp local propagation of chaos for mean field particles with $W^{-1,\infty}$ kernels Wang, Songbo Probability Analysis of PDEs 82C22 (Primary) 60F17, 35Q35 (Secondary) 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. |
| title | Sharp local propagation of chaos for mean field particles with $W^{-1,\infty}$ kernels |
| topic | Probability Analysis of PDEs 82C22 (Primary) 60F17, 35Q35 (Secondary) |
| url | https://arxiv.org/abs/2403.13161 |