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The number of unbounded components in the Poisson Boolean model of continuum percolation in hyperbolic space

Johan Tykesson (Institutionen för matematiska vetenskaper)
Electronic Journal of Probability (1083-6489). Vol. 12 (2007), p. 1379-1401.
[Artikel, refereegranskad vetenskaplig]

We show that for the Poisson Boolean model in hyperbolic space, there are intensities for the underlying Poisson process that produce infinitely many components in the covered region, if the radius of the balls in the model are big enough. In 2 dimensions, this is shown for any radius, and moreover we also consider unbounded components in the vacant region.

Nyckelord: Continuum percolation, hyperbolic space, phase transitions



Denna post skapades 2008-01-10. Senast ändrad 2011-04-01.
CPL Pubid: 65547

 

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