Bivariate asymptotics via random walks: application to large genus maps
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866910123758190592 |
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| author | Price, Andrew Elvey Fang, Wenjie Louf, Baptiste Wallner, Michael |
| author_facet | Price, Andrew Elvey Fang, Wenjie Louf, Baptiste Wallner, Michael |
| contents | We obtain bivariate asymptotics for the number of (unicellular) combinatorial maps (a model of discrete surfaces) as both the size and the genus grow. This work is related to two research topics that have been very active recently: multivariate asymptotics and large genus geometry. Our method consists of studying a linear recurrence for these numbers, and can be applied to many other linear recurrences. In particular, we include a general theorem that yields asymptotics for such recurrences, provided that some assumptions are satisfied. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_06924 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bivariate asymptotics via random walks: application to large genus maps Price, Andrew Elvey Fang, Wenjie Louf, Baptiste Wallner, Michael Combinatorics Probability 05C10, 05C30, 05A16, 60C05 We obtain bivariate asymptotics for the number of (unicellular) combinatorial maps (a model of discrete surfaces) as both the size and the genus grow. This work is related to two research topics that have been very active recently: multivariate asymptotics and large genus geometry. Our method consists of studying a linear recurrence for these numbers, and can be applied to many other linear recurrences. In particular, we include a general theorem that yields asymptotics for such recurrences, provided that some assumptions are satisfied. |
| title | Bivariate asymptotics via random walks: application to large genus maps |
| topic | Combinatorics Probability 05C10, 05C30, 05A16, 60C05 |
| url | https://arxiv.org/abs/2506.06924 |