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arXiv · 1906.01898

Subshifts with leading sequences, uniformity of cocycles and spectra of Schreier graphs

Rostislav Grigorchuk·Daniel Lenz·Tatiana Nagnibeda·Daniel Sell
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Abstract

We introduce a class of subshifts governed by finitely many two-sided infinite words. We call these words leading sequences. We show that any locally constant cocycle over such a subshift is uniform. From this we obtain Cantor spectrum of Lebesgue measure zero for associated Jacobi operators if the subshift is aperiodic. Our class covers all simple Toeplitz subshifts as well as all Sturmian subshifts. We apply our results to the spectral theory of Schreier graphs for uncountable families of groups acting on rooted trees.

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Rostislav Grigorchuk, Daniel Lenz, Tatiana Nagnibeda, Daniel Sell. 2019-06-05. Subshifts with leading sequences, uniformity of cocycles and spectra of Schreier graphs. https://arxiv.org/abs/1906.01898

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