ECP Reading Tools

Trees and Matchings from Point Processes

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Trees and Matchings from Point Processes
2.	Creator	Author's name, affiliation, country	Alexander E. Holroyd; University of California, Berkeley
2.	Creator	Author's name, affiliation, country	Yuval Peres; University of California, Berkeley
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Poisson process, point process, random tree, random matching, minimal spanning forest.
3.	Subject	Subject classification	Primary 60G55; Secondary 60K35.
4.	Description	Abstract	A factor graph of a point process is a graph whose vertices are the points of the process, and which is constructed from the process in a deterministic isometry-invariant way. We prove that the d-dimensional Poisson process has a one-ended tree as a factor graph. This implies that the Poisson points can be given an ordering isomorphic to the usual ordering of the integers in a deterministic isometry-invariant way. For d greater than or equal to 4 our result answers a question posed by Ferrari, Landim and Thorisson [7]. We prove also that any isometry-invariant ergodic point process of finite intensity in Euclidean or hyperbolic space has a perfect matching as a factor graph provided all the inter-point distances are distinct.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2003-03-03
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ecp.ejpecp.org/article/view/1066
10.	Identifier	Digital Object Identifier	10.1214/ECP.v8-1066
11.	Source	Journal/conference title; vol., no. (year)	Electronic Communications in Probability; Vol 8
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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