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The scaling limit of uniform random plane maps, via the Ambjørn–Budd bijection

   
@article{EJP3213,
	author = {Jérémie Bettinelli and Emmanuel Jacob and Grégory Miermont},
	title = {The scaling limit of uniform random plane maps, via the Ambjørn–Budd bijection},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {19},
	year = {2014},
	keywords = {random maps; scaling limits; Brownian map; Gromov-Hausdorff topology; random metric spaces; bijections},
	abstract = {We prove that a uniform rooted plane map with n edges converges in distribution after asuitable normalization to the Brownian map for the Gromov–Hausdorff topology. A recent bijection due to Ambjørn and Budd allows to derive this result by a direct coupling with a uniform random quadrangulation with n faces.},
	pages = {no. 73, 1-16},
	issn = {1083-6489},
	doi = {10.1214/EJP.v19-3213},    
        url = {http://ejp.ejpecp.org/article/view/3213}}