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math.SP2021
On the Correspondence Between Domination and the Spectrum of Jacobi Operators
Kateryna Alkorn, Zhenghe Zhang
In this paper, we first develop a notion of dominated splitting for -sequences and show it is a stable property under -perturbation. Then…
math.SP2020
Schrödinger Operators With Potentials Generated by Hyperbolic Transformations: I. Positivity of the Lyapunov Exponent
Artur Avila, David Damanik, Zhenghe Zhang
We consider discrete one-dimensional Schrödinger operators whose potentials are generated by sampling along the orbits of a general hyperbolic transformation. Specifically, we show…
math.SP2019★ 1 cited
Positive Lyapunov Exponents and a Large Deviation Theorem for Continuum Anderson Models, Briefly
Valmir Bucaj, David Damanik, Jake Fillman +4
In this short note, we prove positivity of the Lyapunov exponent for 1D continuum Anderson models by leveraging some classical tools from inverse spectral theory. The argument is m…