Does a central limit theorem hold for the \(k\)-skeleton of Poisson hyperplanes in hyperbolic space?

DOI10.1007/s00440-021-01032-wzbMath1478.60042arXiv1911.02120OpenAlexW3137476712WikidataQ115607495 ScholiaQ115607495MaRDI QIDQ2663405

Christoph Thäle, Daniel Hug, Felix Herold

Publication date: 16 April 2021

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1911.02120

zbMATH Keywords

central limit theoremU-statisticspair-correlation functionCrofton formulaPoisson hyperplane processhyperbolic stochastic geometry

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Central limit and other weak theorems (60F05) Integral geometry (53C65) Spherical and hyperbolic convexity (52A55) Random convex sets and integral geometry (aspects of convex geometry) (52A22)

Related Items (8)

Random inscribed polytopes in projective geometries ⋮ Variance asymptotics and central limit theory for geometric functionals of Poisson cylinder processes ⋮ The typical cell of a Voronoi tessellation on the sphere ⋮ Beta-star polytopes and hyperbolic stochastic geometry ⋮ Intersections of Poisson \(k\)-flats in constant curvature spaces ⋮ Extremal behavior of large cells in the Poisson hyperplane mosaic ⋮ Large nearest neighbour balls in hyperbolic stochastic geometry ⋮ Faces in random great hypersphere tessellations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Stochastic analysis for Poisson point processes. Malliavin calculus, Wiener-Itô chaos expansions and stochastic geometry
• Normal approximation of Poisson functionals in Kolmogorov distance
• Random conical tessellations
• Fine Gaussian fluctuations on the Poisson space. I: Contractions, cumulants and geometric random graphs
• Limit theory for point processes in manifolds
• A random cell splitting scheme on the sphere
• Integral geometry and geometric inequalities in hyperbolic space
• Multi-dimensional Gaussian fluctuations on the Poisson space
• An analogue of Sylvester's four-point problem on the sphere
• Boundedness of Crofton's cell for the homogeneous Poisson process of geodesics in the hyperbolic plane
• Processes of flats induced by higher dimensional processes
• Wiener chaos: Moments, cumulants and diagrams. A survey with computer implementation
• Central limit theorems for Poisson hyperplane tessellations
• Lectures on hyperbolic geometry
• Hyperuniform states of matter
• Limit theory for isolated and extreme points in hyperbolic random geometric graphs
• Cones generated by random points on half-spheres and convex hulls of Poisson point processes
• Limit theory for the Gilbert graph
• Central limit theorems for \(U\)-statistics of Poisson point processes
• Fine Gaussian fluctuations on the Poisson space. II: Rescaled kernels, marked processes and geometric \(U\)-statistics
• New Berry-Esseen bounds for non-linear functionals of Poisson random measures
• Intersection and proximity of processes of flats
• Splitting tessellations in spherical spaces
• The probability of connectivity in a hyperbolic model of complex networks
• Asymptotics of Visibility in the Hyperbolic Plane
• Visibility to infinity in the hyperbolic plane, despite obstacles
• Invariant Random Fields on Spaces with a Group Action
• Random points in halfspheres
• Random Fields on the Sphere
• Stochastic and Integral Geometry
• On the Intersection Density of Flat Processes
• On the structure of stationary flat processes
• On the structure of stationary flat processes. II
• Invariant Markov Processes Under Lie Group Actions
• Geometric measures for random mosaics in spherical spaces
• Second-Order Theory for Iteration Stable Tessellations
• Mosaïque de Poisson-Voronoi sur une surface
• Hyperuniform and rigid stable matchings
• Asymptotic normality for random polytopes in non-Euclidean geometries
• Moments and Central Limit Theorems for Some Multivariate Poisson Functionals
• The diameter of KPKVB random graphs
• Foundations of Hyperbolic Manifolds
• Lectures on the Poisson Process
• Second‐order properties of the point process of nodes in a stationary Voronoi tessellation
• Integral Geometry in Homogeneous Spaces

This page was built for publication: Does a central limit theorem hold for the \(k\)-skeleton of Poisson hyperplanes in hyperbolic space?