Length spectrum of large genus random metric maps
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866917985374961664 |
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| author | Barazer, Simon Giacchetto, Alessandro Liu, Mingkun |
| author_facet | Barazer, Simon Giacchetto, Alessandro Liu, Mingkun |
| contents | We study the length of short cycles on uniformly random metric maps (also known as ribbon graphs) of large genus using a Teichmüller theory approach. We establish that, as the genus tends to infinity, the length spectrum converges to a Poisson point process with an explicit intensity. This result extends the work of Janson and Louf to the multi-faced case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_10517 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Length spectrum of large genus random metric maps Barazer, Simon Giacchetto, Alessandro Liu, Mingkun Probability Combinatorics Geometric Topology 05C10, 05C80, 32G15, 57M50 We study the length of short cycles on uniformly random metric maps (also known as ribbon graphs) of large genus using a Teichmüller theory approach. We establish that, as the genus tends to infinity, the length spectrum converges to a Poisson point process with an explicit intensity. This result extends the work of Janson and Louf to the multi-faced case. |
| title | Length spectrum of large genus random metric maps |
| topic | Probability Combinatorics Geometric Topology 05C10, 05C80, 32G15, 57M50 |
| url | https://arxiv.org/abs/2312.10517 |