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Stationary random graphs with prescribed iid degrees on a spatial Poisson process


 
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1. Title Title of document Stationary random graphs with prescribed iid degrees on a spatial Poisson process
 
2. Creator Author's name, affiliation, country Maria Deijfen; Stockholm University
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Random graphs, degree distribution, Poisson process, stable matching, stationary model
 
3. Subject Subject classification 05C80; 60G50
 
4. Description Abstract Let $[\mathcal{P}]$ be the points of a Poisson process on $R^d$ and $F$ a probability distribution with support on the non-negative integers. Models are formulated for generating translation invariant random graphs with vertex set $[\mathcal{P}]$ and iid vertex degrees with distribution $F$, and the length of the edges is analyzed. The main result is that finite mean for the total edge length per vertex is possible if and only if $F$ has finite moment of order $(d+1)/d$.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) The Swedish Research Council
 
7. Date (YYYY-MM-DD) 2009-02-16
 
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/1448
 
10. Identifier Digital Object Identifier 10.1214/ECP.v14-1448
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 14
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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