Non-perturbative localization on the strip and Avila's almost reducibility conjecture

Abstract

We prove non-perturbative Anderson localization and almost localization for a family of quasi-periodic operators on the strip. As an application we establish Avila's almost reducibility conjecture for Schr\"odinger operators with trigonometric potentials and all Diophantine frequencies, whose proof for analytic potentials was announced in Avila's 2015 Acta paper. As part of our analysis, we derive a non-selfadjoint version of Haro and Puig's formula connecting Lyapunov exponents of the dual model to those of the original operator.