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Scaling Limits for Random Quadrangulations of Positive Genus

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Scaling Limits for Random Quadrangulations of Positive Genus
2.	Creator	Author's name, affiliation, country	Jérémie L Bettinelli; Université Paris Sud; France
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	random map; random tree; conditioned process; Gromov topology
3.	Subject	Subject classification	60F17
4.	Description	Abstract	Abstract. We discuss scaling limits of large bipartite quadrangulations of positive genus. For a given $g$, we consider, for every positive integer $n$, a random quadrangulation $q_n$ uniformly distributed over the set of all rooted bipartite quadrangulations of genus $g$ with $n$ faces. We view it as a metric space by endowing its set of vertices with the graph distance. We show that, as $n$ tends to infinity, this metric space, with distances rescaled by the factor $n$ to the power of $-1/4$, converges in distribution, at least along some subsequence, toward a limiting random metric space. This convergence holds in the sense of the Gromov-Hausdorff topology on compact metric spaces. We show that, regardless of the choice of the subsequence, the Hausdorff dimension of the limiting space is almost surely equal to $4$. Our main tool is a bijection introduced by Chapuy, Marcus, and Schaeffer between the quadrangulations we consider and objects they call well-labeled $g$-trees. An important part of our study consists in determining the scaling limits of the latter.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2010-10-20
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/810
10.	Identifier	Digital Object Identifier	10.1214/EJP.v15-810
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 15
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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