Hausdorff dimension of visible sets for well-behaved continuum percolation in the hyperbolic plane

Autor(en): Thaele, Christoph
Stichwörter: Boolean model; continuum percolation; fractal geometry; Hausdorff-dimension; hyperbolic geometry; Mathematics; Statistics & Probability
Erscheinungsdatum: 2014
Herausgeber: BRAZILIAN STATISTICAL ASSOCIATION
Journal: BRAZILIAN JOURNAL OF PROBABILITY AND STATISTICS
Volumen: 28
Ausgabe: 1
Startseite: 73
Seitenende: 82
Zusammenfassung: 
Let 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 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 Z. Moreover, the Hausdorff-dimension of the set of (hyperbolic) lines through a fixed point contained in Z is calculated. Thereby several conjectures raised by Benjamini, Jonasson, Schramm and Tykesson are confirmed.
ISSN: 01030752
DOI: 10.1214/12-BJPS194

Show full item record

Page view(s)

1
Last Week
0
Last month
0
checked on Feb 25, 2024

Google ScholarTM

Check

Altmetric