Quantitative estimate of the overdamped limit for the Vlasov–Fokker–Planck systems

Abstract

This note adapts a probabilistic approach to establish a quantified estimate of the overdamped limit for the Vlasov–Fokker–Planck equation towards the aggregation–diffusion equation, which in particular includes cases of the Newtonian type singular forces. The proofs are based on the investigation of the weak convergence of the corresponding stochastic differential equations (SDEs) of Mckean type in the continuous path space. We show that one can recover the same (actually stronger) overdamped limit result as in Choi and Tse (2020) under the same assumptions.

Keywords

• Overdamped
• Large friction
• Zero inertia
• Tightness