Mixing properties and entropy bounds of a family of Pisot random substitutions
We consider a two-parameter family of random substitutions and show certain combinatorial and topological properties they satisfy. We establish that they admit recognisable words at every level. As a consequence, we get that the subshifts they define are not topologically mixing. We then show that t...
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| Main Authors: | , , |
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| 格式: | text |
| 出版: |
Archīum Ateneo
2022
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| 主題: | |
| 在線閱讀: | https://archium.ateneo.edu/mathematics-faculty-pubs/219 https://doi.org/10.1016/j.indag.2022.04.004 |
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| 機構: | Ateneo De Manila University |
| 總結: | We consider a two-parameter family of random substitutions and show certain combinatorial and topological properties they satisfy. We establish that they admit recognisable words at every level. As a consequence, we get that the subshifts they define are not topologically mixing. We then show that they satisfy a weaker mixing property using a numeration system arising from a sequence of lengths of inflated words. Moreover, we provide explicit bounds for the corresponding topological entropy in terms of the defining parameters n and p. |
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