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

2024/06/08 by Yanxue Lin, Lin, Yanxue, Shuzheng Guo +3
Mathematics · #Geometric and Algebraic Topology #Geometric Analysis and Curvature Flows #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2406.05449

Abstract

In this paper, we prove the large deviation estimates and Anderson localization for CMV matrices on ℓ²(ℤ₊) with Verblunsky coefficients defined dynamically by the hyperbolic toral automorphism. Part of positivity results on the Lyapunov exponents of Chulaevsky-Spencer and Anderson localization results of Bourgain-Schlag on Schrödinger operators with strongly mixing potentials are extended to CMV matrices.

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