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arXiv · 2402.00215

Schr\"odinger Operators with Potentials Generated by Hyperbolic Transformations: II. Large Deviations and Anderson Localization

Artur Avila·David Damanik·Zhenghe Zhang
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Abstract

We consider discrete one-dimensional Schr\"odinger operators whose potentials are generated by H\"older continuous sampling along the orbits of a uniformly hyperbolic transformation. For any ergodic measure satisfying a suitable bounded distortion property, we establish a uniform large deviation estimate in a large energy region provided that the sampling function is locally constant or has small supremum norm. We also prove full spectral Anderson localization for the operators in question.

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BibTeXRIS

Artur Avila, David Damanik, Zhenghe Zhang. 2024-01-31. Schr\"odinger Operators with Potentials Generated by Hyperbolic Transformations: II. Large Deviations and Anderson Localization. https://arxiv.org/abs/2402.00215

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