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

   
@article{ECP1448,
	author = {Maria Deijfen},
	title = {Stationary random graphs with prescribed iid degrees on a spatial Poisson process},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {14},
	year = {2009},
	keywords = {Random graphs, degree distribution, Poisson process, stable matching, stationary model},
	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 $(d+1)/d$.},
	pages = {no. 8, 81-89},
	issn = {1083-589X},
	doi = {10.1214/ECP.v14-1448},    
        url = {http://ecp.ejpecp.org/article/view/1448}}