期刊名称：Brazilian Journal of Probability and Statistics
印刷版ISSN：0103-0752
出版年度：2014
卷号：28
期号：1
页码：73-82
DOI：10.1214/12-BJPS194
语种：English
出版社：Brazilian Statistical Association
摘要：Let ${\mathcal{Z}}$ be a so-called well-behaved percolation, that is, a certain random closed set in the hyperbolic plane, whose law is invariant under all isometries; for example, the covered region in a Poisson Boolean model. In terms of the $\alpha$-value of ${\mathcal{Z}}$, the Hausdorff-dimension of the set of directions is determined in which visibility from a fixed point to the ideal boundary of the hyperbolic plane is possible within ${\mathcal{Z}}$. Moreover, the Hausdorff-dimension of the set of (hyperbolic) lines through a fixed point contained in ${\mathcal{Z}}$ is calculated. Thereby several conjectures raised by Benjamini, Jonasson, Schramm and Tykesson are confirmed.
