SCALING LIMIT OF MODERATELY INTERACTING PARTICLE SYSTEMS WITH SINGULAR INTERACTION AND ENVIRONMENTAL NOISE

• 成果类型: Article
• 署名作者: Guo, Shuchen; Luo, Dejun
• 署名单位: Chinese Academy of Sciences
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/22-AAP1860
• 发表日期: 2023
• 页码: 2066-2102
• 关键词: mean-field limit; chaos result; propagation; CONVERGENCE; equation; approximation; DYNAMICS; MODEL

摘要

We consider moderately interacting particle systems with singular inter-action kernel and environmental noise. It is shown that the mollified empirical measures converge in strong norms to the unique (local) solutions of nonlin-ear Fokker-Planck equations. The approach works for the Biot-Savart and repulsive Poisson kernels.