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/√ n converge in the Gromov-Hausdorff sense to 7 √ 2/9 times Aldous' Brownian tree. The proof uses the bijection of Bonichon, Gavoille and Hanusse (J. Graph Algorithms Appl. 9 (2005) 185-204).
The scaling limit of random outerplanar maps
Caraceni A.
2016
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/√ n converge in the Gromov-Hausdorff sense to 7 √ 2/9 times Aldous' Brownian tree. The proof uses the bijection of Bonichon, Gavoille and Hanusse (J. Graph Algorithms Appl. 9 (2005) 185-204).File in questo prodotto:
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