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We prove some asymptotic results for the radius and the profile of largerandom rooted planar maps with faces of arbitrary degrees. Using a bijectiondue to Bouttier, Di Francesco and Guitter between rooted planar maps andcertain four-type trees with positive labels, we derive our results from aconditional limit theorem for four-type spatial Galton-Watson trees.

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