The Scaling Limit of Random Outerplanar Maps

Abstract

A planar map is outerplanar if all its vertices belong to the same face. We show that random uniform outerplanar maps with $n$ vertices suitably rescaled by a factor $1/\sqrt{n}$ converge in the Gromov-Hausdorff sense to $\frac{7\sqrt{2}}{9}$ times Aldous' Brownian tree. The proof uses the bijection of Bonichon, Gavoille and Hanusse.

arXiv comment25 pages