Nonperturbative localization on the strip and Avila’s almost reducibility conjecture

Source abstract

Abstract We prove nonperturbative 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 Schrödinger operators with trigonometric potentials and all Diophantine frequencies. As part of our analysis, we derive a nonselfadjoint version of Haro and Puig’s formula connecting the Lyapunov exponents of the dual model to those of the original operator.