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 41Subject Categories
Probability Theory and Statistics
DOI
10.1214/EJP.v20-3645