Thin Spectra for Periodic and Ergodic Word Models
Spectral Theory
2026-03-04 v2
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.
Keywords
Cite
@article{arxiv.2503.18691,
title = {Thin Spectra for Periodic and Ergodic Word Models},
author = {Jake Fillman and Michala N. Gradner and Hannah J. Hendricks},
journal= {arXiv preprint arXiv:2503.18691},
year = {2026}
}
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21 pages