Radius and profile of random planar maps with faces of arbitrary degrees. (English) Zbl 1190.60024

Miermont, Grégory; Weill, Mathilde

Electron. J. Probab. 13, 79-106 (2008).

Summary: We prove some asymptotic results for the radius and the profile of large random planar maps with faces of arbitrary degrees. Using a bijection due to J. Bouttier, P. Di Francesco and E. Guitter [Electron. J. Comb. 11, No. 1, Research paper R69, 27 p., electronic only (2004; Zbl 1060.05045)] between rooted planar maps and certain four-type trees with positive labels, we derive our results from a conditional limit theorem for four-type spatial Galton-Watson trees.

MSC:

60F17	Functional limit theorems; invariance principles
60J80	Branching processes (Galton-Watson, birth-and-death, etc.)
05C80	Random graphs (graph-theoretic aspects)
60D05	Geometric probability and stochastic geometry

Keywords:

random planar map; invariance principle; multitype spatial galton-watson tree; Brownian snake

Citations:

Zbl 1060.05045