The Scaling Limit of Random Outerplanar Maps

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 $1\mathrm{/}\sqrt{n}$ converge in the Gromov-Hausdorff sense to ${\displaystyle \frac{7\sqrt{2}}{9}}$ times Aldous’ Brownian tree. The proof uses the bijection of Bonichon, Gavoille and Hanusse.