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Asymptotics for Rooted Bipartite Planar Maps and Scaling Limits of Two-Type Spatial Trees

   
@article{EJP425,
	author = {Mathilde Weill},
	title = {Asymptotics for Rooted Bipartite Planar Maps and Scaling Limits of Two-Type Spatial Trees},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {12},
	year = {2007},
	keywords = {Planar maps ; two-type Galton-Watson trees ; Conditioned Brownian snake},
	abstract = {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 tends to infinity, a random $2k$-angulation with n faces has a separating vertex whose removal disconnects the map into two components each with size greater that $n^{1/2 - \varepsilon}$.},
	pages = {no. 31, 862-925},
	issn = {1083-6489},
	doi = {10.1214/EJP.v12-425},    
        url = {http://ejp.ejpecp.org/article/view/425}}