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Stable Poisson Graphs in One Dimension

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Stable Poisson Graphs in One Dimension
2.	Creator	Author's name, affiliation, country	Maria Deijfen; Stockholm University; Sweden
2.	Creator	Author's name, affiliation, country	Alexander E. Holroyd; Microsoft Research; United States
2.	Creator	Author's name, affiliation, country	Yuval Peres; Microsoft Research; United States
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Poisson process; random graph; degree distribution; matching; percolation
3.	Subject	Subject classification	60D05; 05C70; 05C80
4.	Description	Abstract	Let each point of a homogeneous Poisson process on R independently be equipped with a random number of stubs (half-edges) according to a given probability distribution $\mu$ on the positive integers. We consider schemes based on Gale-Shapley stable marriage for perfectly matching the stubs to obtain a simple graph with degree distribution $\mu$. We prove results on the existence of an infinite component and on the length of the edges, with focus on the case $\mu(2)=1$. In this case, for the random direction stable matching scheme introduced by Deijfen and Meester we prove that there is no infinite component, while for the stable matching of Deijfen, Häggström and Holroyd we prove that existence of an infinite component follows from a certain statement involving a finite interval, which is overwhelmingly supported by simulation evidence
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2011-07-06
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/897
10.	Identifier	Digital Object Identifier	10.1214/EJP.v16-897
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 16
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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