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
10836489 (eISSN)
Vol. 20 1-25 41Subject Categories (SSIF 2011)
Probability Theory and Statistics
DOI
10.1214/EJP.v20-3645