Non-simple systoles on random hyperbolic surfaces for large genus
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866918127573401600 |
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| author | He, Yuxin Shen, Yang Wu, Yunhui Xue, Yuhao |
| author_facet | He, Yuxin Shen, Yang Wu, Yunhui Xue, Yuhao |
| contents | In this paper, we investigate the asymptotic behavior of the non-simple systole, which is the length of a shortest non-simple closed geodesic, on a random closed hyperbolic surface on the moduli space $\mathcal{M}_g$ of Riemann surfaces of genus $g$ endowed with the Weil-Petersson measure. We show that as the genus $g$ goes to infinity, the non-simple systole of a generic hyperbolic surface in $\mathcal{M}_g$ behaves exactly like $\log g$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_16447 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Non-simple systoles on random hyperbolic surfaces for large genus He, Yuxin Shen, Yang Wu, Yunhui Xue, Yuhao Geometric Topology Complex Variables Differential Geometry Probability In this paper, we investigate the asymptotic behavior of the non-simple systole, which is the length of a shortest non-simple closed geodesic, on a random closed hyperbolic surface on the moduli space $\mathcal{M}_g$ of Riemann surfaces of genus $g$ endowed with the Weil-Petersson measure. We show that as the genus $g$ goes to infinity, the non-simple systole of a generic hyperbolic surface in $\mathcal{M}_g$ behaves exactly like $\log g$. |
| title | Non-simple systoles on random hyperbolic surfaces for large genus |
| topic | Geometric Topology Complex Variables Differential Geometry Probability |
| url | https://arxiv.org/abs/2308.16447 |