Talk by Matthias Täufer
On October 28th, 2020, Dr. Matthias Täufer (FernUniversität in Hagen) gave a talk about "A robust initial scale estimate and localization at band edges of the continuum Anderson model" as part of the research seminar Analysis of the FernUniversität in Hagen. This lecture is partially supported by the COST action Mathematical models for interacting dynamics on networks.
Abstract
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We prove that Anderson localization near band edges of ergodic continuum random Schrödinger operators with periodic background potential in in dimensions two and larger is universal.
In particular, Anderson localization holds without extra decay assumptions on the random variables and independently of regularity or degeneracy of the Floquet eigenvalues of the background operator.
Our approach is based on a robust initial scale estimate the proof of which avoids Floquet theory altogether and uses instead an interplay between quantitative unique continuation and large deviation estimates.
Furthermore, our reasoning is sufficiently flexible to prove this initial scale estimate in a non-ergodic setting, which promises to be an ingredient for understanding band edge localization also in these situations.
The talk is based on joint work with Albrecht Seelmann (TU Dortmund).
