The number of unbounded components in the Poisson Boolean model in hyperbolic space
Abstract
Description
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.
25 pages, reference added, an error in the introduction corrected, typos corrected
25 pages, reference added, an error in the introduction corrected, typos corrected