Bivariate asymptotics via random walks: application to large genus maps

Fuente: arXiv
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Autores principales: Price, Andrew Elvey, Fang, Wenjie, Louf, Baptiste, Wallner, Michael
Formato: Preprint
Publicado: 2025
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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