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

TL;DR

This paper proves the log-H"older continuity of the Lyapunov exponent for one-dimensional Jacobi operators with skew-shift potentials, using large deviation theorems and the avalanche principle under certain conditions.

Contribution

It establishes the log-H"older continuity of the Lyapunov exponent for Jacobi operators with skew-shift potentials, a novel result in this context.

Findings

Lyapunov exponent is log-H"older continuous under specified conditions.

Large deviation theorem holds for Diophantine frequencies and large disorder.

Combines large deviation theorem with the avalanche principle to prove continuity.

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.