  We consider the homogenization of a Poisson problem or a Stokes system in a
randomly punctured domain with Dirichlet boundary conditions. We assume that
the holes are spherical and have random centres and radii. We impose that the
average distance between the balls is of size $\eps$ and their average radius
is $\varepsilon^{\alpha}$, $\alpha \in (1; 3)$. We prove that, as in the
periodic case [G. Allaire, ``Homogenization of the Navier-Stokes equations in
domains perforated with tiny holes. II''], the solutions converge to the
solution of Darcy's law (or its scalar analogue in the case of Poisson). In the
same spirit of [A. Giunti, R. H\"ofer and J. Vel\'azquez, ``Homogenization of
the Poisson equation in randomly perforated domains under minimal assumptions
on the size of the holes''], we work under minimal conditions on the
integrability of the random radii. These ensure that the problem is
well-defined but do not rule out the onset of clusters of holes.
