Poisson cylinders in hyperbolic space
Probability
2018-03-02 v1
Abstract
We consider the Poisson cylinder model in -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.
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