Thin Spectra for Periodic and Ergodic Word Models

Jake Fillman; Michala N. Gradner; Hannah J. Hendricks

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arXiv · 2503.18691

Thin Spectra for Periodic and Ergodic Word Models

Jake Fillman·Michala N. Gradner·Hannah J. Hendricks

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Abstract

We establish a new and simple criterion that suffices to generate many spectral gaps for periodic word models. This leads to new examples of ergodic Schr\"odinger operators with Cantor spectra having zero Hausdorff dimension that simultaneously may have arbitrarily small supremum norm together with arbitrarily long runs on which the potential vanishes.

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BibTeX RIS

Jake Fillman, Michala N. Gradner, Hannah J. Hendricks. 2025-03-24. Thin Spectra for Periodic and Ergodic Word Models. https://arxiv.org/abs/2503.18691

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