## Electronic Journal of Probability

### Asymptotics for Rooted Bipartite Planar Maps and Scaling Limits of Two-Type Spatial Trees

Mathilde Weill

#### 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 $n^{1/2 - \varepsilon}$.

#### Article information

Source
Electron. J. Probab., Volume 12 (2007), paper no. 31, 862-925.

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

https://projecteuclid.org/euclid.ejp/1464818502

Digital Object Identifier
doi:10.1214/EJP.v12-425

Mathematical Reviews number (MathSciNet)
MR2318414

Zentralblatt MATH identifier
1127.05096

Rights

#### Citation

Weill, Mathilde. Asymptotics for Rooted Bipartite Planar Maps and Scaling Limits of Two-Type Spatial Trees. Electron. J. Probab. 12 (2007), paper no. 31, 862--925. doi:10.1214/EJP.v12-425. https://projecteuclid.org/euclid.ejp/1464818502

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