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On percolation in one-dimensional stable Poisson graphs
Stockholm University, Faculty of Science, Department of Mathematics. Uppsala University, Sweden.
Number of Authors: 3
2015 (English)In: Electronic Communications in Probability, ISSN 1083-589X, E-ISSN 1083-589X, Vol. 20Article in journal (Refereed) Published
Abstract [en]

Equip each point x of a homogeneous Poisson point process P on R with D-x edge stubs, where the D-x are i.i.d. positive integer-valued random variables with distribution given by mu. Following the stable multi-matching scheme introduced by Deijfen, Haggstrom and Holroyd [1], we pair off edge stubs in a series of rounds to form the edge set of a graph G on the vertex set P. In this note, we answer questions of Deijfen, Holroyd and Peres [2] and Deijfen, Haggstrom and Holroyd [1] on percolation (the existence of an infinite connected component) in G. We prove that percolation may occur a.s. even if mu has support over odd integers. Furthermore, we show that for any epsilon > 0, there exists a distribution mu such that mu ({1}) > 1 - epsilon, but percolation still occurs a.s..

Place, publisher, year, edition, pages
2015. Vol. 20
Keyword [en]
Poisson process, Random graph, Matching, Percolation
National Category
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-119129DOI: 10.1214/ECP.v20-3958ISI: 000357151400001OAI: oai:DiVA.org:su-119129DiVA: diva2:843785
Available from: 2015-07-31 Created: 2015-07-29 Last updated: 2017-12-04Bibliographically approved

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