Propagation of chaos for the VPFP equation with a polynomial cut-off

TL;DR

This paper proves the propagation of chaos for a stochastic particle system with polynomial cut-off interactions, providing quantitative error estimates and extending results to less singular forces in the Vlasov-Fokker-Planck equation.

Contribution

It rigorously establishes propagation of chaos for the VPFP system with polynomial cut-off and offers explicit error bounds, extending understanding to less singular interactions.

Findings

Quantitative error estimates between particle system and VPFP solutions

Propagation of chaos holds for polynomial cut-off interactions

Extension to less singular interaction forces in VPFP

Abstract

We consider a $N$-particle system interacting through the Newtonian potential with a polynomial cut-off in the presence of noise in velocity. We rigorously prove the propagation of chaos for this interacting stochastic particle system. Taking the cut-off like $N^{-\delta}$ with $\delta < 1/d$ in the force, we provide a quantitative error estimate between the empirical measure associated to that $N$-particle system and the solutions of the $d$-dimensional Vlasov-Poisson-Fokker-Planck system. We also study the propagation of chaos for the Vlasov-Fokker-Planck equation with less singular interaction forces than the Newtonian one.