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Continuum Percolation at and above the Uniqueness Threshold on Homogeneous Spaces

Johan Tykesson (Institutionen för matematiska vetenskaper, matematisk statistik)
Journal of Theoretical Probability (0894-9840). Vol. 22 (2009), 2, p. 402-417.
[Artikel, refereegranskad vetenskaplig]

We consider the Poisson Boolean model of continuum percolation on a homogeneous space M. Let lambda be the intensity of the underlying Poisson process. Let lambda (u) be the infimum of the set of intensities that a.s. produce a unique unbounded component. First we show that if lambda >lambda (u) , then there is a.s. a unique unbounded component at lambda. Then we let M=H(2)xR and show that at lambda (u) there is a.s. not a unique unbounded component. These results are continuum analogs of theorems by Haggstrom, Peres and Schonmann.

Nyckelord: Continuum percolation, Poisson Boolean model, Uniqueness in, percolation, Mass transport, Homogeneous spaces, infinite clusters, graphs



Denna post skapades 2010-02-25. Senast ändrad 2016-06-30.
CPL Pubid: 115113

 

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Institutioner (Chalmers)

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

Ämnesområden

Matematisk statistik

Chalmers infrastruktur