Asymptotics of Visibility in the Hyperbolic Plane

DOI10.1239/aap/1370870121zbMath1276.60012arXiv1012.5220OpenAlexW2075518771MaRDI QIDQ2837750

Pierre Calka, Johan H. Tykesson

Publication date: 11 July 2013

Published in: Advances in Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1012.5220

zbMATH Keywords

hyperbolic geometryvisibilityBoolean modelPoisson line processPoincaré disc

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items (3)

Does a central limit theorem hold for the \(k\)-skeleton of Poisson hyperplanes in hyperbolic space? ⋮ Beta-star polytopes and hyperbolic stochastic geometry ⋮ Hausdorff dimension of visible sets for well-behaved continuum percolation in the hyperbolic plane

Uses Software

• GVF

Cites Work

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• Boundedness of Crofton's cell for the homogeneous Poisson process of geodesics in the hyperbolic plane
• Dynamical circle covering with homogeneous Poisson updating
• Visibility in the Boolean model
• Random coverings in several dimensions
• Diffusions and random shadows in negatively curved manifolds
• The number of unbounded components in the Poisson Boolean model of continuum percolation in hyperbolic space
• Visibility to infinity in the hyperbolic plane, despite obstacles
• Recouvrements aléatoires et théorie du potentiel
• Very large graphs
• Contact and chord length distribution of a stationary Voronoi tessellation
• The distributions of the smallest disks containing the Poisson-Voronoi typical cell and the Crofton cell in the plane
• On Second‐Order Characteristics of Germ‐Grain Models with Convex Grains
• On the second derivative of the spherical contact distribution function of smooth grain models

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