Publication: The Spectrum of Schrödinger Operators with Randomly Perturbed Ergodic Potentials
The Spectrum of Schrödinger Operators with Randomly Perturbed Ergodic Potentials
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Avila, A., Damanik, D., & Gorodetski, A. (2023). The Spectrum of Schrödinger Operators with Randomly Perturbed Ergodic Potentials. Geometric and Functional Analysis, 33(2), 364–375. https://doi.org/10.1007/s00039-023-00632-z
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We consider Schrödinger operators in ℓ2(Z) whose potentials are given by the sum of an ergodic term and a random term of Anderson type. Under the assumption that the ergodic term is generated by a homeomorphism of a connected compact metric space and a continuous sampling function, we show that the almost sure spectrum arises in an explicitly described way from the unperturbed spectrum and the topological support of the single-site distribution. In particular, assuming that the latter is compact and contains at least two points, this
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- Avila, Artur
- Damanik, David
- Gorodetski, Anton
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Avila, A., Damanik, D., & Gorodetski, A. (2023). The Spectrum of Schrödinger Operators with Randomly Perturbed Ergodic Potentials. Geometric and Functional Analysis, 33(2), 364–375. https://doi.org/10.1007/s00039-023-00632-z