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Stationary random graphs on $Z$ with prescribed iid degrees and finite mean connections

   
@article{ECP1239,
	author = {Maria Deijfen and Johan Jonasson},
	title = {Stationary random graphs on $Z$ with prescribed iid  degrees and finite mean connections},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {11},
	year = {2006},
	keywords = {Random graphs; degree distribution;  stationary model},
	abstract = {Let $F$ be a probability distribution with support on the non-negative integers. A model is proposed for generating stationary simple graphs on $Z$ with degree distribution $F$ and it is shown for this model that the expected total length of all edges at a given vertex is finite if $F$ has finite second moment. It is not hard to see that any stationary model for generating simple graphs on $Z$ will give infinite mean for the total edge length per vertex if $F$ does not have finite second moment. Hence, finite second moment of $F$ is a necessary and sufficient condition for the existence of a model with finite mean total edge length.},
	pages = {no. 33, 336-346},
	issn = {1083-589X},
	doi = {10.1214/ECP.v11-1239},    
        url = {http://ecp.ejpecp.org/article/view/1239}}