On expected face numbers of random beta and beta' polytopes

DOI10.1007/s13366-022-00626-2OpenAlexW4210987798MaRDI QIDQ2689459

Zakhar Kabluchko

Publication date: 10 March 2023

Published in: Beiträge zur Algebra und Geometrie (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2107.06655

zbMATH Keywords

\(f\)-vectorStirling numbersstochastic geometryrecurrence relationsrandom polytopesolid anglebeta distributionbeta prime distributionrandom cone

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Bell and Stirling numbers (11B73) Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.) (52B05) (n)-dimensional polytopes (52B11) Recurrences (11B37) Other functions defined by series and integrals (33E20) Other functions coming from differential, difference and integral equations (33E30) Spherical and hyperbolic convexity (52A55) Approximation by convex sets (52A27) Random convex sets and integral geometry (aspects of convex geometry) (52A22)

Related Items (1)

Face numbers of high-dimensional Poisson zero cells

Cites Work

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• Stochastical approximation of convex bodies
• A canonical decomposition of the probability measure of sets of isotropic random points in \(\mathbb{R}^n\)
• Random projections of regular simplices
• Beta polytopes and Poisson polyhedra: \(f\)-vectors and angles
• Faces in random great hypersphere tessellations
• Angles of random simplices and face numbers of random polytopes
• Recursive scheme for angles of random simplices, and applications to random polytopes
• Cones generated by random points on half-spheres and convex hulls of Poisson point processes
• The typical cell of a Voronoi tessellation on the sphere
• Random points in halfspheres
• Random polytopes in a ball
• Expected intrinsic volumes and facet numbers of random beta‐polytopes
• Angle sums of random simplices in dimensions 3 and 4
• Isotropic random simplices
• EXPECTEDf‐VECTOR OF THE POISSON ZERO POLYTOPE AND RANDOM CONVEX HULLS IN THE HALF‐SPHERE

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