Higher order return times for $ϕ$-mixing measures
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912651402018816 |
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| author | Haydn, Nicolai T A Park, Gin |
| author_facet | Haydn, Nicolai T A Park, Gin |
| contents | In this paper we consider $ϕ$-mixing measures and show that the limiting return times distribution is compound Poisson distribution as the target sets shrink to a zero measure set. The approach we use generalises a method given by Galves and Schmitt in 1997 for the first entry time to higher orders. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_14116 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Higher order return times for $ϕ$-mixing measures Haydn, Nicolai T A Park, Gin Probability Dynamical Systems 37A50, 37A25, 60F05, 60G70 In this paper we consider $ϕ$-mixing measures and show that the limiting return times distribution is compound Poisson distribution as the target sets shrink to a zero measure set. The approach we use generalises a method given by Galves and Schmitt in 1997 for the first entry time to higher orders. |
| title | Higher order return times for $ϕ$-mixing measures |
| topic | Probability Dynamical Systems 37A50, 37A25, 60F05, 60G70 |
| url | https://arxiv.org/abs/2510.14116 |