Electronic Communications in Probability

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

Maria Deijfen

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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 $(d+1)/d$.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465234717

Digital Object Identifier
doi:10.1214/ECP.v14-1448

Mathematical Reviews number (MathSciNet)
MR2481668

Zentralblatt MATH identifier
1185.05126

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

Keywords
Random graphs degree distribution Poisson process stable matching stationary model

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

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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