uu.seUppsala University Publications
Change search
ReferencesLink to record
Permanent link

Direct link
Connectedness of Poisson cylinders in Euclidean space
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
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) PublishedText
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
URN: urn:nbn:se:uu:diva-277773DOI: 10.1214/14-AIHP641ISI: 000368564900006OAI: oai:DiVA.org:uu-277773DiVA: diva2:905859
Swedish Research CouncilKnut and Alice Wallenberg Foundation
Available from: 2016-02-23 Created: 2016-02-23 Last updated: 2016-02-23Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full text

Search in DiVA

By author/editor
Broman, Erik I.
By organisation
Department of Mathematics
In the same journal
Annales de l'I.H.P. Probabilites et statistiques
Probability Theory and Statistics

Search outside of DiVA

GoogleGoogle Scholar
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Altmetric score

Total: 65 hits
ReferencesLink to record
Permanent link

Direct link