  This contribution is concerned with the effective viscosity problem, that is,
the homogenization of the steady Stokes system with a random array of rigid
particles, for which the main difficulty is the treatment of close particles.
Standard approaches in the literature have addressed this issue by making
moment assumptions on interparticle distances. Such assumptions however prevent
clustering of particles, which is not compatible with physically-relevant
particle distributions. In this contribution, we take a different perspective
and consider moment bounds on the size of clusters of close particles. On the
one hand, assuming such bounds, we construct correctors and prove
homogenization (using a variational formulation and $\Gamma$-convergence to
avoid delicate pressure issues). On the other hand, based on subcritical
percolation techniques, these bounds are shown to hold for various mixing
particle distributions with nontrivial clustering. As a by-product of the
analysis, we also obtain similar homogenization results for compressible and
incompressible linear elasticity with unbounded random stiffness.
