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

Time: Thu 2019-01-24 14.00 - 15.00

Lecturer: Marius Lemm, Institute for Advanced Study, IAS

Location: Seminar Hall Kuskvillan, Institut Mittag-Leffler

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.

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Last changed: Jan 23, 2019