Positivity of the Lyapunov exponent for analytic quasiperiodic operators with arbitrary finite-valued background

Abstract

We study lower bounds on the Lyapunov exponent associated with one-frequency quasiperiodic Schr\"odinger operators with an added finite valued background potential. We prove that, for sufficiently large coupling constant, the Lyapunov exponent is positive with a uniform (in energy and background) minoration.