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math.SP2021★ 1 cited
Localization and Cantor spectrum for quasiperiodic discrete Schrödinger operators with asymmetric, smooth, cosine-like sampling functions
Yakir Forman, Tom VandenBoom
We prove Cantor spectrum and almost-sure Anderson localization for quasiperiodic discrete Schrödinger operators with potential sampled with Diophantine fr…
math.SP2019
Finite-gap CMV matrices: Periodic coordinates and a Magic Formula
Jacob S. Christiansen, Benjamin Eichinger, Tom VandenBoom
We prove a bijective unitary correspondence between 1) the isospectral torus of almost-periodic, absolutely continuous CMV matrices having fixed finite-gap spectrum and 2) special…
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…