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 Electronic Communications in Probability > Vol. 14 (2009) > Paper 8 open journal systems 


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

Maria Deijfen, Stockholm University


Abstract
Let $[mathcal{P}]$ be the points of a Poisson process on $RR^d$ 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 $(d+1)/d$.


Full text: PDF

Pages: 81-89

Published on: February 16, 2009
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Electronic Communications in Probability. ISSN: 1083-589X