Séminaire Lotharingien de Combinatoire, 93B.3 (2025), 12 pp.
Andrew Elvey Price, Wenjie Fang, Baptiste Louf and Michael Wallner
Bivariate Asymptotics via Random Walks: Application to Large Genus Maps
Abstract.
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 in studying a linear recurrence for these numbers, and in fact it can be applied to many other linear recurrences. We discuss briefly the generality of our method and future research directions.
Received: November 15, 2024.
Accepted: February 15, 2025.
Final version: April 1, 2025.
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