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.
PLANE
Statistics & Probability
hyperbolic space
RANDOM INTERLACEMENTS
PERCOLATION
Poisson cylinders
continuum percolation
Author
Erik Broman
Uppsala Universitet
Johan Tykesson
Chalmers, Mathematical Sciences, Mathematical Statistics
University of Gothenburg
Electronic Journal of Probability
1083-6489 (ISSN)
Vol. 20 1-25 41Subject Categories (SSIF 2011)
Probability Theory and Statistics
DOI
10.1214/EJP.v20-3645