2018/04/19 by Hui Huang, Huang, Hui, Jian‐Guo Liu +3 · 1 citation
Economics, Econometrics and Finance · Engineering · Mathematics · #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Gas Dynamics and Kinetic Theory #Mathematical Physics (math-ph) #Particle Dynamics in Fluid Flows #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1804.07002
openalex publication_date 2018/04/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We rigorously justify the mean-field limit of a N-particle system subject to the Brownian motion and interacting through a Newtonian potential in ℝ3. Our result leads to a derivation of the Vlasov-Poisson-Fokkker-Planck (VPFP) equation from the microscopic N-particle system. More precisely, we show that the maximal distance between the exact microscopic trajectories and trajectories following the the mean-field is bounded by N-(1)/(3)+ε ((1)/(63)≤ε0. Moreover, we prove the convergence rate between the empirical measure associated to the particle system and the solution of the VPFP equations. The technical novelty of this paper is that our estimates crucially rely on the randomness coming from the initial data and from the Brownian motion.