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.
2016-01-01

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).
Settore MAT/06 - Probabilita' e Statistica Matematica
Brownian continuum random tree; Galton-Watson trees; Gromov-Hausdorff topology; Random outerplanar maps; Scaling limits
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/125563
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