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Stable Poisson Graphs in One Dimension
Stockholm University, Faculty of Science, Department of Mathematics.
2011 (English)In: Electronic Journal of Probability, ISSN 1083-6489, Vol. 16, 1238-1253 p.Article in journal (Refereed) Published
Abstract [en]

Let each point of a homogeneous Poisson process on R independently be equipped with a random number of stubs (half-edges) according to a given probability distribution mu on the positive integers. We consider schemes based on Gale-Shapley stable marriage for perfectly matching the stubs to obtain a simple graph with degree distribution mu. We prove results on the existence of an infinite component and on the length of the edges, with focus on the case mu({2}) = 1. In this case, for the random direction stable matching scheme introduced by Deijfen and Meester we prove that there is no infinite component, while for the stable matching of Deijfen, Haggstrom and Holroyd we prove that existence of an infinite component follows from a certain statement involving a finite interval, which is overwhelmingly supported by simulation evidence

Place, publisher, year, edition, pages
2011. Vol. 16, 1238-1253 p.
Keyword [en]
Poisson process, random graph, degree distribution, matching, percolation
National Category
URN: urn:nbn:se:su:diva-66571ISI: 000293023900001OAI: diva2:468757
authorCount :3Available from: 2011-12-21 Created: 2011-12-20 Last updated: 2011-12-21Bibliographically approved

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