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Pré-Publication, Document De Travail Année : 2006

Asymptotics for rooted planar maps and scaling limits of two-type spatial trees

Résumé

We prove some asymptotic results for the radius and the profile of large random bipartite planar maps. Using a bijection due to Bouttier, Di Francesco and Guitter between rooted bipartite planar maps and certain two-type trees with positive labels, we derive our results from a conditional limit theorem for two-type spatial trees. Finally we apply our estimates to separating vertices of bipartite planar maps: with probability close to one when $n$ goes to infinity, a random $2\ka$-angulation with $n$ faces has a separating vertex whose removal disconnects the map into two components each with size greater that $n^{1/2-\vep}$.
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Dates et versions

hal-00093173 , version 1 (12-09-2006)

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Mathilde Weill. Asymptotics for rooted planar maps and scaling limits of two-type spatial trees. 2006. ⟨hal-00093173⟩
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