Anderson localization for the quasi-periodic CMV matrices with Verblunsky coefficients defined by the skew-shift

Abstract: In this paper, we study quasi-periodic CMV matrices with Verblunsky coefficients given by the skew-shift. We prove the positivity of Lyapunov exponents and Anderson localization for most frequencies, which establish the analogous results of one-dimensional Schr\"{o}dinger operators proved by Bourgain, Goldstein and Schlag.