EXPECTEDf‐VECTOR OF THE POISSON ZERO POLYTOPE AND RANDOM CONVEX HULLS IN THE HALF‐SPHERE

DOI10.1112/mtk.12056zbMath1530.52008arXiv1901.10528OpenAlexW3080146149MaRDI QIDQ6134986

Zakhar Kabluchko

Publication date: 23 August 2023

Published in: Mathematika (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1901.10528

zbMATH Keywords

half-spherePoisson hyperplane tessellationrandom convex hullsexpected \(f\)-vector

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.) (52B05) (n)-dimensional polytopes (52B11) Polyhedra and polytopes; regular figures, division of spaces (51M20) Spherical and hyperbolic convexity (52A55) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20) Random convex sets and integral geometry (aspects of convex geometry) (52A22)

Related Items (12)

Random inscribed polytopes in projective geometries ⋮ Face numbers of high-dimensional Poisson zero cells ⋮ Weak convergence of the intersection point process of Poisson hyperplanes ⋮ The typical cell of a Voronoi tessellation on the sphere ⋮ Beta-star polytopes and hyperbolic stochastic geometry ⋮ On expected face numbers of random beta and beta' polytopes ⋮ Convex geometry and its applications. Abstracts from the workshop held December 12--18, 2021 (hybrid meeting) ⋮ Angles of random simplices and face numbers of random polytopes ⋮ Recursive scheme for angles of random simplices, and applications to random polytopes ⋮ Faces in random great hypersphere tessellations ⋮ Facial structure of strongly convex sets generated by random samples ⋮ A new approach to weak convergence of random cones and polytopes

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