Marius Lemm: On the averaged Green's function of an elliptic equation with random coefficients

Abstract: We consider a divergence-form elliptic difference operator on the lattice \(Z^d\), with a coefficient matrix that is a random perturbation of the identity matrix. Recently, Bourgain introduced novel techniques from harmonic analysis to study the averaged Green's function of this model. Our main contribution is a refinement of Bourgain's approach which improves the key decay rate from \(−2d+\epsilon \) to \(−3d+\epsilon\).

This talk is an extended version of one given at the kick-off conference and will present the main ideas in the proof, in particular Bourgain's disjointification trick.