Continuum Percolation in Stochastic Homogenization and the Effective Viscosity Problem

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