Gaussian polytopes: variances and limit theorems

DOI10.1239/aap/1118858627zbMath1089.52003OpenAlexW2045924955MaRDI QIDQ5694146

Daniel Hug, Matthias Reitzner

Publication date: 29 September 2005

Published in: Advances in Applied Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1239/aap/1118858627

zbMATH Keywords

variancenormal distributionconvex hulllimit theoremintrinsic volumerandom point

Mathematics Subject Classification ID

Multivariate distribution of statistics (62H10) Geometric probability and stochastic geometry (60D05) Combinatorial probability (60C05) Random convex sets and integral geometry (aspects of convex geometry) (52A22)

Related Items (17)

Central limit theorems for Gaussian polytopes ⋮ Gaussian polytopes: a cumulant-based approach ⋮ Exploring stochasticity and imprecise knowledge based on linear inequality constraints ⋮ Convex hulls of random walks: expected number of faces and face probabilities ⋮ A theory of capacity and sparse neural encoding ⋮ Facets of high-dimensional Gaussian polytopes ⋮ Stars of empty simplices ⋮ The smoothed complexity of Frank-Wolfe methods via conditioning of random matrices and polytopes ⋮ Small-ball probabilities for the volume of random convex sets ⋮ Poincaré inequality in mean value for Gaussian polytopes ⋮ Correction to: ``Central limit theorems for Gaussian polytopes ⋮ Intrinsic volumes and Gaussian polytopes: the missing piece of the jigsaw ⋮ Approximation of convex sets by polytopes ⋮ Expected volumes of Gaussian polytopes, external angles, and multiple order statistics ⋮ Variance asymptotics and scaling limits for Gaussian polytopes ⋮ Gaussian convex bodies: a nonasymptotic approach ⋮ Thin-shell theory for rotationally invariant random simplices

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• [https://portal.mardi4nfdi.de/wiki/Publication:5728818 �ber die konvexe H�lle von n zuf�llig gew�hlten Punkten]

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