Abstract
We consider moderately interacting particle systems with singular interaction kernel and environmental noise. It is shown that the mollified empirical measures converge in strong norms to the unique (local) solutions of nonlinear Fokker–Planck equations. The approach works for the Biot–Savart and repulsive Poisson kernels.
Funding Statement
The second named author was supported by the National Key R&D Program of China (No. 2020YFA0712700), the National Natural Science Foundation of China (Nos. 11931004, 12090014), and the Youth Innovation Promotion Association, CAS (Y2021002).
Citation
Shuchen Guo. Dejun Luo. "Scaling limit of moderately interacting particle systems with singular interaction and environmental noise." Ann. Appl. Probab. 33 (3) 2066 - 2102, June 2023. https://doi.org/10.1214/22-AAP1860
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