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arXiv · 1405.1971

The Scaling Limit of Random Outerplanar Maps

Alessandra Caraceni
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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 $\displaystyle{\frac{7 \sqrt{2}}{9}}$ times Aldous' Brownian tree. The proof uses the bijection of Bonichon, Gavoille and Hanusse.

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Alessandra Caraceni. 2014-05-08. The Scaling Limit of Random Outerplanar Maps. https://arxiv.org/abs/1405.1971

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