Connectedness of Poisson cylinders in Euclidean space
Artikel i vetenskaplig tidskrift, 2016

We consider the Poisson cylinder model in R-d, d >= 3. We show that given any two cylinders c(1) and c(2) in the process, there is a sequence of at most d - 2 other cylinders creating a connection between c(1) and c(2). In particular, this shows that the union of the cylinders is a connected set, answering a question appearing in (Probab. Theory Related Fields 154 (2012) 165-191). We also show that there are cylinders in the process that are not connected by a sequence of at most d - 3 other cylinders. Thus, the diameter of the cluster of cylinders equals d - 2.

Poisson cylinder model

Continuum percolation

Författare

Erik Broman

Uppsala universitet

Johan Tykesson

Chalmers, Matematiska vetenskaper, matematisk statistik

Göteborgs universitet

Annales de linstitut Henri Poincare (B) Probability and Statistics

0246-0203 (ISSN)

Vol. 52 1 102-126

Ämneskategorier

Matematik

DOI

10.1214/14-AIHP641