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

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