Localization for the Anderson model

Event time: 
Wednesday, October 3, 2018 - 4:15pm
Location: 
LOM 215
Speaker: 
Charlie Smart
Speaker affiliation: 
University of Chicago
Event description: 

Title:  Localization for the Anderson model

Abstract:  Anderson localization is a physical phenomenon in which electron transport in amorphous solid materials is inhibited by the presence of disorder.  The Anderson model for this phenomenon consists of the Laplacian on a lattice perturbed by a random potential.  After briefly discussing the mathematical theory of the Anderson model, I will explain my recent joint work with Jian Ding.  We prove that, in the case of a Bernoulli potential and a two dimensional lattice, the eigenfunctions near the edge of the spectrum are exponentially localized.  A key ingredient is a new unique continuation result for eigenfunctions of random Hamiltonians in dimension two.