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arXiv · 2406.05449

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

Yanxue Lin·Shuzheng Guo·Daxiong Piao
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Abstract

In this paper, we prove the large deviation estimates and Anderson localization for CMV matrices on $\ell^2(\mathbb{Z}_+)$ 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 Schr\"{o}dinger operators with strongly mixing potentials are extended to CMV matrices.

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Yanxue Lin, Shuzheng Guo, Daxiong Piao. 2024-06-08. Anderson localization for CMV matrices with Verblunsky coefficients defined by the hyperbolic toral automorphism. https://arxiv.org/abs/2406.05449

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