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

Maria Deijfen ; Johan Jonasson (Institutionen för matematiska vetenskaper)
Electronic Communications in Probability (1083-589X). Vol. 11 (2006), p. 336-346.
[Artikel, refereegranskad vetenskaplig]

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.

Denna post skapades 2007-01-12. Senast ändrad 2011-04-01.
CPL Pubid: 25484


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