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

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

2006-10-05

arxiv.org/abs/math/0610202v3

Electronic Journal of Probability 2007, Vol. 12, pp. 1379-1401

Mathematics

Probability

25 pages, reference added, an error in the introduction corrected, typos corrected

Scientific paper

We consider the Poisson Boolean continuum percolation model in n-dimensional hyperbolic space. In 2 dimensions we show that there are intensities for the underlying Poisson process for which there are infinitely unbounded components in the covered and vacant regions. In n dimensions we show that if the radius of the balls are big enough, then there are intensities for the underlying Poisson process for which there are infinitely many unbounded components.

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