English

Poisson cylinders in hyperbolic space

Probability 2018-03-02 v1

Abstract

We consider the Poisson cylinder model in dd-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.

Keywords

Cite

@article{arxiv.1803.00354,
  title  = {Poisson cylinders in hyperbolic space},
  author = {Erik I. Broman and Johan H. Tykesson},
  journal= {arXiv preprint arXiv:1803.00354},
  year   = {2018}
}

Comments

29 pages

R2 v1 2026-06-23T00:38:05.176Z