Log-H\"older Continuity of the Lyapunov Exponent for Jacobi Operators with Potentials Given by the Skew-Shift

Abstract

In this paper we study one-dimensional Jacobi operators on the lattice with a potential given by the skew shift. We show that the large deviation theorem takes place for Diophantine frequency and sufficiently large disorder. Combining the large deviation theorem with the avalanche principle, we prove the log-H\"older continuity of the Lyapunov exponent.