Constructing Toeplitz arrays via cut and project schemes
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909974430482432 |
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| author | Cortez, María Isabel Drewlo, Jamal Gómez, Jaime Jäger, Tobias |
| author_facet | Cortez, María Isabel Drewlo, Jamal Gómez, Jaime Jäger, Tobias |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_19921 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Constructing Toeplitz arrays via cut and project schemes Cortez, María Isabel Drewlo, Jamal Gómez, Jaime Jäger, Tobias Dynamical Systems 37B05, 37B10, 52C23 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. |
| title | Constructing Toeplitz arrays via cut and project schemes |
| topic | Dynamical Systems 37B05, 37B10, 52C23 |
| url | https://arxiv.org/abs/2512.19921 |