The number of unbounded components in the Poisson Boolean model in hyperbolic space
Probability
2007-11-05 v3
Abstract
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.
Cite
@article{arxiv.math/0610202,
title = {The number of unbounded components in the Poisson Boolean model in hyperbolic space},
author = {Johan Tykesson},
journal= {arXiv preprint arXiv:math/0610202},
year = {2007}
}
Comments
25 pages, reference added, an error in the introduction corrected, typos corrected