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Some families of increasing planar maps

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Some families of increasing planar maps
2.	Creator	Author's name, affiliation, country	Marie Albenque; LIAFA, Université Paris 7
2.	Creator	Author's name, affiliation, country	Jean-Francois Marckert; LaBRI, Université Bordeaux
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	stackmaps, triangulations, Gromov-Hausdorff convergence, continuum random tree
3.	Subject	Subject classification	60C05, 60F1
4.	Description	Abstract	Stack-triangulations appear as natural objects when one wants to define some families of increasing triangulations by successive additions of faces. We investigate the asymptotic behavior of rooted stack-triangulations with $2n$ faces under two different distributions. We show that the uniform distribution on this set of maps converges, for a topology of local convergence, to a distribution on the set of infinite maps. In the other hand, we show that rescaled by $n^{1/2}$, they converge for the Gromov-Hausdorff topology on metric spaces to the continuum random tree introduced by Aldous. Under a distribution induced by a natural random construction, the distance between random points rescaled by $(6/11)\log n$ converge to 1 in probability. We obtain similar asymptotic results for a family of increasing quadrangulations.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	The second author was partially supported by the French Agence Nationale de la Recherche, project SADA ANR-05-BLAN-0372.
7.	Date	(YYYY-MM-DD)	2008-09-19
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/563
10.	Identifier	Digital Object Identifier	10.1214/EJP.v13-563
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 13
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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