Localization for random CMV matrices
Xiaowen Zhu
TL;DR
This paper proves Anderson localization and dynamical localization in expectation for random CMV matrices with arbitrary i.i.d. Verblunsky coefficients, advancing understanding of spectral properties in random unitary operators.
Contribution
It establishes localization results for random CMV matrices with general i.i.d. Verblunsky coefficients, extending previous work to broader distributions.
Findings
Proves Anderson localization for random CMV matrices.
Establishes dynamical localization in expectation.
Applicable to arbitrary i.i.d. Verblunsky coefficient distributions.
Abstract
We prove Anderson localization (AL) and dynamical localization in expectation (EDL, also known as strong dynamical localization) for random CMV matrices for arbitrary distribution of i.i.d. Verblunsky coefficients.
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Taxonomy
TopicsRandom Matrices and Applications · Spectral Theory in Mathematical Physics · Numerical methods in inverse problems