Stochastic Homogenization and Energy of Infinite Sets of Points
Xavier Blanc · 2008
Abstract This chapter presents, in a synthetic way, a series of recent works by X. Blanc, C. Le Bris, and P-L. Lions on homogenization of an elliptic partial differential equation under certain periodic or random assumptions. The coefficients are non-constant but are a stationary random deformation of a periodic set of coefficients; a limit is taken where the period (in d-space) of the periodicity shrinks to zero. The chapter also describes related work on average energies of nonperiodic infinite sets of points.