Poisson cylinders in hyperbolic space
Journal article, 2015

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.

RANDOM INTERLACEMENTS

PERCOLATION

Statistics & Probability

Poisson cylinders

PLANE

continuum percolation

hyperbolic space

Author

Erik Broman

Uppsala University

Johan Tykesson

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematical Statistics

Electronic Journal of Probability

1083-6489 (ISSN)

Vol. 20 1-25 41

Subject Categories

Probability Theory and Statistics

DOI

10.1214/EJP.v20-3645

More information

Latest update

2/28/2018