Spectra of infinite Cayley graphs, examples with pure band spectra

Pierre de la Harpe

Spectra of infinite Cayley graphs, examples with pure band spectra

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arxiv 2402.06279 v1 pith:DJE7PNMK submitted 2024-02-09 math.CO

Pierre de la Harpe This is my paper · ORCID

classification math.CO

keywords cayleygammaspectraadjacencyarbitrarilybanddisjointexamples

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abstract

It is shown that there are groups $\Gamma$ with finite generating sets $S$ such that the adjacency operator of the Cayley graph ${\rm Cay}(\Gamma,S)$ is a disjoint union of $N$ intervals, for arbitrarily large integers $N$.

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Random Schr\"odinger operators and convolution on wreath products
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Averaged spectral measures of a class of random Schrödinger operators coincide with Plancherel measures of convolution operators on wreath products, yielding new spectral criteria and Lifshitz tail estimates.

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