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

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

2006-09-12

arxiv.org/abs/math/0609334v1

Mathematics

Probability

Scientific paper

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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