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.
Søren Fournais
Aarhus University
Rupert Frank
LMU Munich
Benjamin Schlein
University of Zurich, UZH
Simone Warzel
TU Munich


Rupert Frank


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