Asymptotic normality of pattern counts in random maps II
Combinatorics
2026-03-23 v1 Discrete Mathematics
Abstract
In a recent work, a central limit theorem for pattern counts in random planar maps was proven by reducing the problem to a face count problem. We provide a shorter proof by circumventing this reduction through the computation of bivariate coefficient asymptotics from a functional equation with one catalytic variable and extend the result to pattern counts with arbitrary boundary and new map classes.
Cite
@article{arxiv.2603.19485,
title = {Asymptotic normality of pattern counts in random maps II},
author = {Eva-Maria Hainzl},
journal= {arXiv preprint arXiv:2603.19485},
year = {2026}
}