On the Dynamical Localization of Random Band Matrices

Abstract

This paper will provide an overview on the Mermin-Wagner Style shift methodology used by Cipolloni, Peled, Schenker, and Shapiro in their proof of Anderson Localization for the Wegner W-orbital model at localization length << W^4. It provides insights into how this technique can be adapted towards other RBM systems including two alternative models. In doing so, the paper suggests a new shift methodology that can potentially show localization at stricter lengths for some generalized systems.