Measure of the spectra of periodic graph operators in the large-coupling limit

Jake Fillman

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arXiv · 2511.00757

Measure of the spectra of periodic graph operators in the large-coupling limit

Jake Fillman

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Abstract

We derive a sharp criterion on the spectra of periodic discrete Schr\"odinger operators acting on connected periodic lattices: the measure of the spectrum goes to zero as the coupling constant goes to infinity if and only if there is no infinite connected path of degeneracies.

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Jake Fillman. 2025-11-02. Measure of the spectra of periodic graph operators in the large-coupling limit. https://arxiv.org/abs/2511.00757

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