  This work develops a quantitative homogenization theory for random
suspensions of rigid particles in a steady Stokes flow, and completes recent
qualitative results. More precisely, we establish a large-scale regularity
theory for this Stokes problem, and we prove moment bounds for the associated
correctors and optimal estimates on the homogenization error; the latter
further requires a quantitative ergodicity assumption on the random suspension.
Compared to the corresponding quantitative homogenization theory for
divergence-form linear elliptic equations, substantial difficulties arise from
the analysis of the fluid incompressibility and the particle rigidity
constraints. Our analysis further applies to the problem of stiff inclusions in
(compressible or incompressible) linear elasticity and in electrostatics; it is
also new in those cases, even in the periodic setting.
