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Anderson localization for quasi-periodic CMV matrices and quantum walks
We consider CMV matrices, both standard and extended, with analytic quasi-periodic Verblunsky coefficients and prove Anderson localization in the regime of positive Lyapunov exponents. This establishes the CMV analog of a ...
Anderson localization for radial tree graphs with random branching numbers
We prove Anderson localization for the discrete Laplace operator on radial tree graphs with random branching numbers. Our method relies on the representation of the Laplace operator as the direct sum of half-lineﾠJacobi ...
Limit-periodic Schrödinger operators with Lipschitz continuous IDS
(American Mathematical Society, 2019)
We show that there exist limit-periodic Schrödinger operators such that the associated integrated density of states is Lipschitz continuous. These operators arise in the inverse spectral theoretic KAM approach of Pöschel.
Multidimensional Almost-Periodic Schrödinger Operators with Cantor Spectrum
We construct multidimensional almost-periodic Schrödinger operators whose spectrum has zero lower box-counting dimension. In particular, the spectrum in these cases is a generalized Cantor set of zero Lebesgue measure.