Intersections of Poisson \(k\)-flats in constant curvature spaces
DOI10.1016/j.spa.2023.08.001zbMath1525.60059arXiv2302.09524OpenAlexW4385989107MaRDI QIDQ6080376
Daniel Hug, Carina Betken, Christoph Thäle
Publication date: 30 October 2023
Published in: Stochastic Processes and their Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2302.09524
stochastic geometrycentral limit theoremintegral geometryU-statisticconstant curvature spacePoisson \(k\)-flat process
Geometric probability and stochastic geometry (60D05) Central limit and other weak theorems (60F05) Integral geometry (53C65) Spherical and hyperbolic convexity (52A55) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55) Random convex sets and integral geometry (aspects of convex geometry) (52A22)
Cites Work
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- Normal approximation of Poisson functionals in Kolmogorov distance
- Some inequalities for chord power integrals of parallelotopes
- On the largest component of a hyperbolic model of complex networks
- Maximum and minimum sets for some geometric mean values
- Random inscribed polytopes in projective geometries
- Wiener chaos: Moments, cumulants and diagrams. A survey with computer implementation
- Lectures on hyperbolic geometry
- Anchored expansion, speed and the Poisson-Voronoi tessellation in symmetric spaces
- Law of large numbers for the largest component in a hyperbolic model of complex networks
- Sharp inequalities for functional integrals and traces of conformally invariant operators.
- Cases of equality in the Riesz rearrangement inequality
- Limit theory for isolated and extreme points in hyperbolic random geometric graphs
- Clustering in a hyperbolic model of complex networks
- Faces in random great hypersphere tessellations
- Anchored expansion of Delaunay complexes in real hyperbolic space and stationary point processes
- Central limit theorems for \(U\)-statistics of Poisson point processes
- The dual Brunn-Minkowski theory for bounded Borel sets: dual affine quermassintegrals and inequalities
- Rearrangement inequalities for functionals with monotone integrands
- New Berry-Esseen bounds for non-linear functionals of Poisson random measures
- Intersection and proximity of processes of flats
- Splitting tessellations in spherical spaces
- Does a central limit theorem hold for the \(k\)-skeleton of Poisson hyperplanes in hyperbolic space?
- The typical cell of a Voronoi tessellation on the sphere
- Beta-star polytopes and hyperbolic stochastic geometry
- Symmetrization in Analysis
- Curvature Measures
- Stochastic and Integral Geometry
- Existence and Uniqueness of the Minimizing Solution of Choquard's Nonlinear Equation
- Local Stereology
- Poisson-Voronoi tessellations in three-dimensional hyperbolic spaces
- Sub-tree counts on hyperbolic random geometric graphs
- Foundations of Modern Probability
- Asymptotic normality for random polytopes in non-Euclidean geometries
- Moments and Central Limit Theorems for Some Multivariate Poisson Functionals
- Foundations of Hyperbolic Manifolds
- Lectures on the Poisson Process
- Convex Bodies The Brunn-MinkowskiTheory
- Integral Geometry in Homogeneous Spaces
- Comparison theorems for exit times
- The critical probability for Voronoi percolation in the hyperbolic plane tends to 1/2
