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April 2012 Percolation in invariant Poisson graphs with i.i.d. degrees
Maria Deijfen, Olle Häggström, Alexander E. Holroyd
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Ark. Mat. 50(1): 41-58 (April 2012). DOI: 10.1007/s11512-010-0139-8


Let each point of a homogeneous Poisson process in ℝd independently be equipped with a random number of stubs (half-edges) according to a given probability distribution μ on the positive integers. We consider translation-invariant schemes for perfectly matching the stubs to obtain a simple graph with degree distribution μ. Leaving aside degenerate cases, we prove that for any μ there exist schemes that give only finite components as well as schemes that give infinite components. For a particular matching scheme which is a natural extension of Gale–Shapley stable marriage, we give sufficient conditions on μ for the absence and presence of infinite components.


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Maria Deijfen. Olle Häggström. Alexander E. Holroyd. "Percolation in invariant Poisson graphs with i.i.d. degrees." Ark. Mat. 50 (1) 41 - 58, April 2012.


Received: 6 February 2010; Published: April 2012
First available in Project Euclid: 31 January 2017

zbMATH: 1254.05181
MathSciNet: MR2890343
Digital Object Identifier: 10.1007/s11512-010-0139-8

Rights: 2011 © Institut Mittag-Leffler

Vol.50 • No. 1 • April 2012
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