## Electronic Communications in Probability

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

#### 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.

#### Article information

Source
Electron. Commun. Probab., Volume 11 (2006), paper no. 33, 336-346.

Dates
Accepted: 5 December 2006
First available in Project Euclid: 4 June 2016

https://projecteuclid.org/euclid.ecp/1465058876

Digital Object Identifier
doi:10.1214/ECP.v11-1239

Mathematical Reviews number (MathSciNet)
MR2274528

Zentralblatt MATH identifier
1127.05093

Subjects
Secondary: 60G50: Sums of independent random variables; random walks

Rights

#### Citation

Deijfen, Maria; Jonasson, Johan. Stationary random graphs on $Z$ with prescribed iid degrees and finite mean connections. Electron. Commun. Probab. 11 (2006), paper no. 33, 336--346. doi:10.1214/ECP.v11-1239. https://projecteuclid.org/euclid.ecp/1465058876

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