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We study the homogenization of the Dirichlet problem for the Stokes equationsin $\mathbb{R}^3$ perforated by $m$ spherical particles. We assume thepositions and velocities of the particles to be identically and independentlydistributed random variables. In the critical regime, when the radii of theparticles are of order $m^{-1}$, the homogenization limit $u$ is given as thesolution to the Brinkman equations. We provide optimal rates for theconvergence $u_m \to u$ in $L^2$, namely $m^{-\beta}$ for all $\beta < 1/2$.Moreover, we consider the fluctuations. In the central limit scaling, we showthat these converge to a Gaussian field, locally in $L^2(\mathbb{R}^3)$, withan explicit covariance.  Our analysis is based on explicit approximations for the solutions $u_m$ interms of $u$ as well as the particle positions and their velocities. These areshown to be accurate in $\dot H^1(\mathbb{R}^3)$ to order $m^{-\beta}$ for all$\beta < 1$. Our results also apply to the analogous problem regarding thehomogenization of the Poisson equations.

Convergence rates and fluctuations for the Stokes-Brinkman equations as homogenization limit in perforated domains