Correlation functions of the Rudin-Shapiro sequence
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866912661059403776 |
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| author | Mazáč, Jan |
| author_facet | Mazáč, Jan |
| contents | In this paper, we show that all odd-point correlation functions of the balanced Rudin--Shapiro sequence vanish and that all even-point correlation functions depend only on a single number, which holds for any weighted correlation function as well. For the four-point correlation functions, we provide a more detailed exposition which reveals some arithmetic structures and symmetries. In particular, we show that one can obtain the autocorrelation coefficients of its topological factor with maximal pure point spectrum among them. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_01090 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Correlation functions of the Rudin-Shapiro sequence Mazáč, Jan Dynamical Systems 37B10, 52C23 In this paper, we show that all odd-point correlation functions of the balanced Rudin--Shapiro sequence vanish and that all even-point correlation functions depend only on a single number, which holds for any weighted correlation function as well. For the four-point correlation functions, we provide a more detailed exposition which reveals some arithmetic structures and symmetries. In particular, we show that one can obtain the autocorrelation coefficients of its topological factor with maximal pure point spectrum among them. |
| title | Correlation functions of the Rudin-Shapiro sequence |
| topic | Dynamical Systems 37B10, 52C23 |
| url | https://arxiv.org/abs/2211.01090 |