  We rigorously justify the mean-field limit of a $N$-particle system subject
to the Brownian motion and interacting through a Newtonian potential in
$\mathbb{R}^3$. 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 $N^{-\frac{1}{3}+\varepsilon}$
($\frac{1}{63}\leq\varepsilon<\frac{1}{36}$) for a system with blob size
$N^{-\delta}$ ($\frac{1}{3}\leq\delta<\frac{19}{54}-\frac{2\varepsilon}{3}$) up
to a probability $1-N^{-\alpha}$ for any $\alpha>0$. 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.
