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arXiv · 0706.3334

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

Grégory Miermont·Mathilde Weill
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Abstract

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.

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Grégory Miermont, Mathilde Weill. 2007-06-22. Radius and profile of random planar maps with faces of arbitrary degrees. https://arxiv.org/abs/0706.3334

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