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2015 Poisson cylinders in hyperbolic space
Erik Broman, Johan Tykesson
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Electron. J. Probab. 20: 1-25 (2015). DOI: 10.1214/EJP.v20-3645

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.

 

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Erik Broman. Johan Tykesson. "Poisson cylinders in hyperbolic space." Electron. J. Probab. 20 1 - 25, 2015. https://doi.org/10.1214/EJP.v20-3645

Information

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

zbMATH: 1333.60198
MathSciNet: MR3335832
Digital Object Identifier: 10.1214/EJP.v20-3645

Subjects:
Primary: 60K35
Secondary: 82B43

Keywords: continuum percolation , Hyperbolic space

JOURNAL ARTICLE
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