Central limit theorems for Poisson hyperplane tessellations

DOI10.1214/105051606000000033zbMath1132.60023arXivmath/0607120OpenAlexW2080746292MaRDI QIDQ997957

Volker Schmidt, Lothar Heinrich, Hendrik Schmidt

Publication date: 8 August 2007

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0607120

zbMATH Keywords

point processcentral limit theorem\(U\)-statisticHoeffding's decompositionPoisson hyperplane process\(k\)-flat intersection process

Mathematics Subject Classification ID

Asymptotic properties of parametric estimators (62F12) Geometric probability and stochastic geometry (60D05) Central limit and other weak theorems (60F05)

Related Items (16)

On strongly rigid hyperfluctuating random measures ⋮ Berry-Esseen bounds and Cramér-type large deviations for the volume distribution of Poisson cylinder processes ⋮ Variance asymptotics and central limit theory for geometric functionals of Poisson cylinder processes ⋮ Weak convergence of the intersection point process of Poisson hyperplanes ⋮ Hyperuniform states of matter ⋮ Asymptotic Methods for Random Tessellations ⋮ Does a central limit theorem hold for the \(k\)-skeleton of Poisson hyperplanes in hyperbolic space? ⋮ U-Statistics in Stochastic Geometry ⋮ Extremal behavior of large cells in the Poisson hyperplane mosaic ⋮ Central limit theorems for \(U\)-statistics of Poisson point processes ⋮ Refined convergence for the Boolean model ⋮ Limit theorems for functionals on the facets of stationary random tessellations ⋮ Moments and Central Limit Theorems for Some Multivariate Poisson Functionals ⋮ Empirical (Typical) Cells of the Poisson Medial Tessellation ⋮ Second moment formulae for geometric sampling with test probes ⋮ Central Limit Theorems for Volume and Surface Content of Stationary Poisson Cylinder Processes in Expanding Domains

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