Connectedness of Poisson cylinders in Euclidean space

@article{Broman2013ConnectednessOP,
  title={Connectedness of Poisson cylinders in Euclidean space},
  author={E. Broman and Johan Tykesson},
  journal={Annales De L Institut Henri Poincare-probabilites Et Statistiques},
  year={2013},
  volume={52},
  pages={102-126}
}
  • E. Broman, Johan Tykesson
  • Published 2013
  • Mathematics
  • Annales De L Institut Henri Poincare-probabilites Et Statistiques
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… Expand
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