Scaling limits of random outerplanar maps with independent link-weights
Probability
2016-12-12 v2 Combinatorics
Abstract
The scaling limit of large simple outerplanar maps was established by Caraceni using a bijection due to Bonichon, Gavoille and Hanusse. The present paper introduces a new bijection between outerplanar maps and trees decorated with ordered sequences of edge-rooted dissections of polygons. We apply this decomposition in order to provide a new, short proof of the scaling limit that also applies to the general setting of first-passage percolation. We obtain sharp tail-bounds for the diameter and recover the asymptotic enumeration formula for outerplanar maps. Our methods also enable us treat subclasses such as bipartite outerplanar maps.
Keywords
Cite
@article{arxiv.1505.07600,
title = {Scaling limits of random outerplanar maps with independent link-weights},
author = {Benedikt Stufler},
journal= {arXiv preprint arXiv:1505.07600},
year = {2016}
}