多项式截断下VPFP方程的混沌传播
Propagation of chaos for the VPFP equation with a polynomial cut-off
摘要：
研究了具有速度噪声的$N$ -粒子系统通过多项式截断的牛顿位势的相互作用.我们严格证明了这种相互作用的随机粒子系统的混沌传播。取截断的类$N^{-δ}$，力中有$δ< 1/d$，我们给出了$N$ -粒子系统的经验测度与$d$ -维Vlasov-Poisson-Fokker-Planck系统的解之间的定量误差估计.我们还研究了具有比牛顿方程更小的奇异相互作用力的Vlasov-Fokker-Planck方程的混沌传播。
英文摘要：
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 $N^{-δ}$ with $δ< 1/d$ 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
