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2007 Asymptotics for Rooted Bipartite Planar Maps and Scaling Limits of Two-Type Spatial Trees
Mathilde Weill
Author Affiliations +
Electron. J. Probab. 12: 862-925 (2007). DOI: 10.1214/EJP.v12-425

Abstract

We prove some asymptotic results for the radius and the profile of large random bipartite planar maps. Using a bijection due to Bouttier, Di Francesco and Guitter between rooted bipartite planar maps and certain two-type trees with positive labels, we derive our results from a conditional limit theorem for two-type spatial trees. Finally we apply our estimates to separating vertices of bipartite planar maps: with probability close to one when n tends to infinity, a random $2k$-angulation with n faces has a separating vertex whose removal disconnects the map into two components each with size greater that $n^{1/2 - \varepsilon}$.

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Mathilde Weill. "Asymptotics for Rooted Bipartite Planar Maps and Scaling Limits of Two-Type Spatial Trees." Electron. J. Probab. 12 862 - 925, 2007. https://doi.org/10.1214/EJP.v12-425

Information

Accepted: 13 June 2007; Published: 2007
First available in Project Euclid: 1 June 2016

zbMATH: 1127.05096
MathSciNet: MR2318414
Digital Object Identifier: 10.1214/EJP.v12-425

Subjects:
Primary: 05C80
Secondary: 60F17, 60J80

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Vol.12 • 2007
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