Non-stationary Furstenberg Theorem and Anderson Localization

22.06.2022, 13:30  –  Haus 9, Raum 0.17 und Zoom
Forschungsseminar Diskrete Spektraltheorie

Anton Gorodetski (UCI)

Abstract: In this talk we will formulate a non-stationary version of the Furstenberg Theorem on random matrix products. As a main application we will discuss how it can be used to prove a non-stationary version of Anderson Localization. Specifically, for discrete Schrodinger operators on $\ell²(\mathbb{Z})$ with bounded random but not necessarily identically distributed values of the potential one can show spectral localization (with exponentially decaying eigenfunctions) as well as dynamical localization. No regularity assumptions on the distributions are required. The results were obtained jointly with Victor Kleptsyn (CNRS).