Anderson localization for CMV matrices with Verblunsky coefficients defined by the hyperbolic toral automorphism

Abstract

In this paper, we prove the large deviation estimates and Anderson localization for CMV matrices on ${\ell }^2\left(Z_{+}\right)$ with Verblunsky coefficients defined dynamically by the hyperbolic toral automorphism. Part of positivity results on the Lyapunov exponents of Chulaevsky-Spencer [9] and Anderson localization results of Bourgain-Schlag [6] on Schrödinger operators with strongly mixing potentials are extended to CMV matrices.