In this paper we consider the mean field limit and non-relativistic limit of relativistic Vlasov-Maxwell particle system to Vlasov-Poisson equation. With the relativistic Vlasov-Maxwell particle system being a starting point, we carry out the estimates (with respect to $N$ and $c$) between the characteristic equation of both Vlasov-Maxwell particle model and Vlasov-Poisson equation, where the probabilistic method is exploited. In the last step, we take both large $N$ limit and non-relativistic limit (meaning $c$ tending to infinity) to close the argument.

中文翻译：

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Vlasov-Maxwell粒子系统到Vlasov-Poisson系统的组合平均场极限和非相对论极限

在本文中，我们考虑了相对论 Vlasov-Maxwell 粒子系统对 Vlasov-Poisson 方程的平均场极限和非相对论极限。以相对论 Vlasov-Maxwell 粒子系统为起点，我们在 Vlasov-Maxwell 粒子模型的特征方程和 Vlasov-Poisson 方程之间进行估计（关于 $N$ 和 $c$），其中概率方法被利用。在最后一步，我们同时采用大 $N$ 极限和非相对论极限（意味着 $c$ 趋于无穷大）来结束论证。