A "lifting" method for exponential large deviation estimates and an application to certain non-stationary 1D lattice Anderson models

Abstract

Proofs of localization for random Schrödinger operators with sufficiently regular distribution of the potential can take advantage of the fractional moment method introduced by Aizenman-Molchanov, or use the classical Wegner estimate as part of another method, e.g. the multi-scale analysis introduced by Fröhlich-Spencer and significantly developed by Klein and his collaborators. When the potential distribution is singular, most proofs rely crucially on exponential estimates of events corresponding to finite truncations of the operator in question; these estimates in some sense substitute for the classical Wegner estimate. We introduce a method to "lift" such estimates, which have been obtained for many stationary models, to certain closely related non-stationary models. As an application, we use this method to derive Anderson localization on the 1-D lattice for certain non-stationary potentials along the lines of the non-perturbative approach developed by Jitomirskaya-Zhu in 2019.

arXiv commentReferee comments integrated, funding information updated, citations updated, typos fixed

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Cited by in corpus (2)

• Localization and unique continuation for non-stationary Schrödinger operators on the 2D lattice
• Localization of the 1D Non-Stationary Anderson Model