Connectedness of Poisson cylinders in Euclidean space
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
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.
Poisson cylinder model, Continuum percolation
Probability Theory and Statistics
IdentifiersURN: urn:nbn:se:uu:diva-277773DOI: 10.1214/14-AIHP641ISI: 000368564900006OAI: oai:DiVA.org:uu-277773DiVA: diva2:905859
FunderSwedish Research CouncilKnut and Alice Wallenberg Foundation