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Connectedness of Poisson cylinders in Euclidean space

Erik Broman ; Johan Tykesson (Institutionen för matematiska vetenskaper, matematisk statistik)
Annales De L Institut Henri Poincare-Probabilites Et Statistiques (0246-0203). Vol. 52 (2016), 1, p. 102-126.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: Poisson cylinder model, Continuum percolation



Denna post skapades 2016-02-17. Senast ändrad 2016-06-30.
CPL Pubid: 232142

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematisk statistik (2005-2016)

Ämnesområden

Matematik

Chalmers infrastruktur