Electronic Communications in Probability

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

Maria Deijfen

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

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

Rights

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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