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Poisson cylinders in hyperbolic space
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
2015 (English)In: Electronic Journal of Probability, ISSN 1083-6489, E-ISSN 1083-6489, Vol. 20, 1-25 p.Article in journal (Refereed) Published
Abstract [en]

We consider the Poisson cylinder model in d-dimensional hyperbolic space. We show that in contrast to the Euclidean case, there is a phase transition in the connectivity of the collection of cylinders as the intensity parameter varies. We also show that for any non-trivial intensity, the diameter of the collection of cylinders is infinite.

Place, publisher, year, edition, pages
2015. Vol. 20, 1-25 p.
Keyword [en]
Poisson cylinders, hyperbolic space, continuum percolation
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-252168DOI: 10.1214/EJP.v20-3645ISI: 000352582100001OAI: oai:DiVA.org:uu-252168DiVA: diva2:810216
Available from: 2015-05-06 Created: 2015-05-04 Last updated: 2017-12-04Bibliographically approved

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Broman, Erik

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