Non-perturbative weak Hölder continuity of Lyapunov exponent of discrete analytic Jacobi operators with skew-shift mapping

Abstract

In this article, we study the continuity of the Lyapunov exponent of discrete analytic Jacobi operators with the skew-shift mapping. We prove that the Lyapunov exponent is weak Holder continuous in E for any Diophantine frequency in the large coupling regimes.