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arXiv · 2512.19921

Constructing Toeplitz arrays via cut and project schemes

María Isabel Cortez·Jamal Drewlo·Jaime Gómez·Tobias Jäger
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Abstract

We show a one-to-one correspondence between Toeplitz arrays over residually finite topological groups and model sets obtained via specific cut and project schemes, built from the odometer associated to the Toeplitz array. As an application, we construct irregular Toeplitz arrays which are extensions of maximal rank $k$ over their maximal equicontinuous factor (given by the associated odometer) and have exactly $k$ different ergodic measures. A modification of the construction also allows to obtain examples with the same measure-theoretic structure, but infinite maximal rank.

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María Isabel Cortez, Jamal Drewlo, Jaime Gómez, Tobias Jäger. 2025-12-22. Constructing Toeplitz arrays via cut and project schemes. https://arxiv.org/abs/2512.19921

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