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 Bouttier, Di Francesco & 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.
Grégory Miermont. Mathilde Weill. "Radius and profile of random planar maps with faces of arbitrary degrees." Electron. J. Probab. 13 79 - 106, 2008. https://doi.org/10.1214/EJP.v13-478