Electronic Communications in Probability

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

Maria Deijfen

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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 $(d+1)/d$.

Article information

Electron. Commun. Probab., Volume 14 (2009), paper no. 8, 81-89.

Accepted: 16 February 2009
First available in Project Euclid: 6 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 05C80: Random graphs [See also 60B20]
Secondary: 60G50: Sums of independent random variables; random walks

Random graphs degree distribution Poisson process stable matching stationary model

This work is licensed under aCreative Commons Attribution 3.0 License.


Deijfen, Maria. Stationary random graphs with prescribed iid degrees on a spatial Poisson process. Electron. Commun. Probab. 14 (2009), paper no. 8, 81--89. doi:10.1214/ECP.v14-1448. https://projecteuclid.org/euclid.ecp/1465234717

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