Quantitative estimates of propagation of chaos for stochastic systems with W-1,∞ kernels

• 成果类型: Article
• 署名作者: Jabin, Pierre-Emmanuel; Wang, Zhenfu
• 署名单位: University System of Maryland; University of Maryland College Park; University System of Maryland; University of Maryland College Park; University of Pennsylvania
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-018-0808-y
• 发表日期: 2018
• 页码: 523-591
• 关键词: mean-field limit; point-vortex method; particle approximation; gradient flows; diffusing particles; gamma-convergence; large deviations; landau equation; EXISTENCE; DYNAMICS

摘要

We derive quantitative estimates proving the propagation of chaos for large stochastic systems of interacting particles. We obtain explicit bounds on the relative entropy between the joint law of the particles and the tensorized law at the limit. We have to develop for this new laws of large numbers at the exponential scale. But our result only requires very weak regularity on the interaction kernel in the negative Sobolev space W--1,W-infinity thus including the Biot-Savart law and the point vortices dynamics for the 2d incompressible Navier-Stokes.