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Percolation in invariant Poisson graphs with i.i.d. degrees

Journal article
Authors M. Deijfen
Olle Häggström
A. E. Holroyd
Published in Arkiv for Matematik
Volume 50
Issue 1
Pages 41-58
ISSN 0004-2080
Publication year 2012
Published at Department of Mathematical Sciences, Mathematical Statistics
Pages 41-58
Language en
Links dx.doi.org/10.1007/s11512-010-0139-...
Keywords stationary random graphs, prescribed iid degrees, nearest-neighbor, degree sequence
Subject categories Mathematics

Abstract

Let each point of a homogeneous Poisson process in R-d independently be equipped with a random number of stubs (half-edges) according to a given probability distribution mu on the positive integers. We consider translation-invariant schemes for perfectly matching the stubs to obtain a simple graph with degree distribution mu. Leaving aside degenerate cases, we prove that for any mu 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 mu for the absence and presence of infinite components.

Page Manager: Webmaster|Last update: 9/11/2012
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