Limit theorems for the typical Poisson-Voronoi cell and the Crofton cell with a large inradius

DOI10.1214/009117905000000134zbMath1084.60008arXivmath/0507463OpenAlexW4297119611MaRDI QIDQ2569231

Pierre Calka, Tomasz Schreiber

Publication date: 18 October 2005

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

Full work available at URL: https://arxiv.org/abs/math/0507463

zbMATH Keywords

extreme pointPalm distributionlarge and moderate deviationsrandom convex hullsGerm-grain models

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Large deviations (60F10) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items (19)

Cluster size distributions of extreme values for the Poisson-Voronoi tessellation ⋮ Intersections of random sets ⋮ Distance from the nucleus to a uniformly random point in the 0-cell and the typical cell of the Poisson-Voronoi tessellation ⋮ Asymptotic Methods for Random Tessellations ⋮ Introduction to Stochastic Geometry ⋮ Concentration and moderate deviations for Poisson polytopes and polyhedra ⋮ Faces of Poisson-Voronoi mosaics ⋮ Asymptotic statistics of then-sided planar Poisson–Voronoi cell: II. Heuristics ⋮ Planar discrete birth-growth Poisson–Voronoi tessellations with the von Neumann neighbourhood ⋮ Random line tessellations of the plane: Statistical properties of many-sided cells ⋮ Asymptotic shape of small cells ⋮ Empirical means for the Voronoi tessellations of the Poincaré disc. ⋮ Life after life. Remembering Tomasz Schreiber ⋮ Asymptotic statistics of then-sided planar Poisson–Voronoi cell: I. Exact results ⋮ Large deviation probabilities for the number of vertices of random polytopes in the ball ⋮ Sylvester’s question and the random acceleration process ⋮ Large planar Poisson-Voronoi cells containing a given convex body ⋮ Fractal random series generated by Poisson-Voronoi tessellations ⋮ Elongated Poisson-Voronoi cells in an empty half-plane

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