Connectedness of Poisson cylinders in Euclidean space

  title={Connectedness of Poisson cylinders in Euclidean space},
  author={E. Broman and Johan Tykesson},
  journal={Annales De L Institut Henri Poincare-probabilites Et Statistiques},
  • 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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Percolation in the vacant set of Poisson cylinders
Geometry of the random interlacement
Geometry of the Uniform Spanning Forest: Transitions in Dimensions 4, 8, 12
Connectivity properties of random interlacement and intersection of random walks
Vacant Set of Random Interlacements and Percolation
Cylinders’ percolation in three dimensions
Continuum percolation (Cambridge University Press)
  • 1996