On the averaged Green's function of an elliptic equation with random coefficients
Spectral Methods in Mathematical Physics
24 January 14:00 - 15:00
Marius Lemm - Institute for Advanced Study, IAS
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.
University of Zurich, UZH