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Connectedness of Poisson cylinders in Euclidean space
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
Chalmers, Dept Math, Gothenburg, Sweden.;Gothenburg Univ, S-41124 Gothenburg, Sweden..
2016 (English)In: Annales de l'I.H.P. Probabilites et statistiques, ISSN 0246-0203, E-ISSN 1778-7017, Vol. 52, no 1, 102-126 p.Article in journal (Refereed) Published
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Abstract [en]

We consider the Poisson cylinder model in R-d, d >= 3. We show that given any two cylinders c(1) and c(2) in the process, there is a sequence of at most d - 2 other cylinders creating a connection between c(1) and c(2). In particular, this shows that the union of the cylinders is a connected set, answering a question appearing in (Probab. Theory Related Fields 154 (2012) 165-191). We also show that there are cylinders in the process that are not connected by a sequence of at most d - 3 other cylinders. Thus, the diameter of the cluster of cylinders equals d - 2.

Place, publisher, year, edition, pages
2016. Vol. 52, no 1, 102-126 p.
Keyword [en]
Poisson cylinder model, Continuum percolation
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:uu:diva-277773DOI: 10.1214/14-AIHP641ISI: 000368564900006OAI: oai:DiVA.org:uu-277773DiVA: diva2:905859
Funder
Swedish Research CouncilKnut and Alice Wallenberg Foundation
Available from: 2016-02-23 Created: 2016-02-23 Last updated: 2017-11-30Bibliographically approved

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Broman, Erik I.

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