Radius and profile of random planar maps with faces of arbitrary degrees

Grégory Miermont (1) , Mathilde Weill (2)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay
2 DMA - Département de Mathématiques et Applications - ENS Paris

We prove some asymptotic results for the radius and the profile of large random rooted planar maps with faces of arbitrary degrees. Using a bijection due to Bouttier, Di Francesco and Guitter 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.

Mots clés: Random planar map; invariance principle; multitype spatial Galton-Watson tree; Brownian snake

Domaines: Probabilités [math.PR]

Grégory Miermont, Mathilde Weill. Radius and profile of random planar maps with faces of arbitrary degrees. Electronic Journal of Probability, 2008, 13, pp.79--106. ⟨hal-00156788⟩