Lengths of saddle connections on random translation surfaces of large genus
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
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| _version_ | 1866914027811110912 |
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| author | Masur, Howard Rafi, Kasra Randecker, Anja |
| author_facet | Masur, Howard Rafi, Kasra Randecker, Anja |
| contents | We determine the distribution of the number of saddle connections on a random translation surface of large genus. More specifically, for genus $g$ tending to infinity, the number of saddle connections with lengths in a given interval $[\frac{a}{g}, \frac{b}{g}]$ converges in distribution to a Poisson distributed random variable. Furthermore, the numbers of saddle connections associated to disjoint intervals of lengths are independent. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_08727 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lengths of saddle connections on random translation surfaces of large genus Masur, Howard Rafi, Kasra Randecker, Anja Geometric Topology Probability 32G15 30F60 57M50 We determine the distribution of the number of saddle connections on a random translation surface of large genus. More specifically, for genus $g$ tending to infinity, the number of saddle connections with lengths in a given interval $[\frac{a}{g}, \frac{b}{g}]$ converges in distribution to a Poisson distributed random variable. Furthermore, the numbers of saddle connections associated to disjoint intervals of lengths are independent. |
| title | Lengths of saddle connections on random translation surfaces of large genus |
| topic | Geometric Topology Probability 32G15 30F60 57M50 |
| url | https://arxiv.org/abs/2412.08727 |