Poisson genericity in numeration systems with exponentially mixing probabilities
Fuente:
arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911055211397120 |
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| author | Álvarez, Nicolás Becher, Verónica Cesaratto, Eda Mereb, Martín Peres, Yuval Weiss, Benjamin |
| author_facet | Álvarez, Nicolás Becher, Verónica Cesaratto, Eda Mereb, Martín Peres, Yuval Weiss, Benjamin |
| contents | We define Poisson genericity for infinite sequences in any finite or countable alphabet with an invariant exponentially-mixing probability measure. A sequence is Poisson generic if the number of occurrences of blocks of symbols asymptotically follows a Poisson law as the block length increases. We prove that almost all sequences are Poisson generic. Our result generalizes Peres and Weiss' theorem about Poisson genericity of integral bases numeration systems. In particular, we obtain that their continued fraction expansions for almost all real numbers are Poisson generic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_04116 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Poisson genericity in numeration systems with exponentially mixing probabilities Álvarez, Nicolás Becher, Verónica Cesaratto, Eda Mereb, Martín Peres, Yuval Weiss, Benjamin Probability Number Theory 60g55, 11k16 We define Poisson genericity for infinite sequences in any finite or countable alphabet with an invariant exponentially-mixing probability measure. A sequence is Poisson generic if the number of occurrences of blocks of symbols asymptotically follows a Poisson law as the block length increases. We prove that almost all sequences are Poisson generic. Our result generalizes Peres and Weiss' theorem about Poisson genericity of integral bases numeration systems. In particular, we obtain that their continued fraction expansions for almost all real numbers are Poisson generic. |
| title | Poisson genericity in numeration systems with exponentially mixing probabilities |
| topic | Probability Number Theory 60g55, 11k16 |
| url | https://arxiv.org/abs/2411.04116 |