Electronic Journal of Probability

Poisson cylinders in hyperbolic space

Erik Broman and Johan Tykesson

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Abstract

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.

 

Article information

Source
Electron. J. Probab., Volume 20 (2015), paper no. 41, 25 pp.

Dates
Accepted: 9 April 2015
First available in Project Euclid: 4 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1465067147

Digital Object Identifier
doi:10.1214/EJP.v20-3645

Mathematical Reviews number (MathSciNet)
MR3335832

Zentralblatt MATH identifier
1333.60198

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 82B43: Percolation [See also 60K35]

Keywords
Hyperbolic space continuum percolation

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Broman, Erik; Tykesson, Johan. Poisson cylinders in hyperbolic space. Electron. J. Probab. 20 (2015), paper no. 41, 25 pp. doi:10.1214/EJP.v20-3645. https://projecteuclid.org/euclid.ejp/1465067147


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