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2009 Stationary random graphs with prescribed iid degrees on a spatial Poisson process
Maria Deijfen
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Electron. Commun. Probab. 14: 81-89 (2009). DOI: 10.1214/ECP.v14-1448

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 $(d+1)/d$.

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Maria Deijfen. "Stationary random graphs with prescribed iid degrees on a spatial Poisson process." Electron. Commun. Probab. 14 81 - 89, 2009. https://doi.org/10.1214/ECP.v14-1448

Information

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

zbMATH: 1185.05126
MathSciNet: MR2481668
Digital Object Identifier: 10.1214/ECP.v14-1448

Subjects:
Primary: 05C80
Secondary: 60G50

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