Intrinsic volumes and Gaussian polytopes: the missing piece of the jigsaw

DOI10.25537/dm.2017v22.1323-1335zbMath1385.60021arXiv1606.07945MaRDI QIDQ683762

Imre Bárány, Christoph Thäle

Publication date: 9 February 2018

Published in: Documenta Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1606.07945

zbMATH Keywords

random polytopesGaussian polytopesvariance lower bound

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Integral geometry (53C65) Random convex sets and integral geometry (aspects of convex geometry) (52A22)

Related Items (5)

Facets of high-dimensional Gaussian polytopes ⋮ Asymptotic normality for random polytopes in non-Euclidean geometries ⋮ Random polytopes: Central limit theorems for intrinsic volumes ⋮ High-dimensional limit theorems for random vectors in ℓpn-balls. II ⋮ A new approach to weak convergence of random cones and polytopes

Cites Work

• Variance asymptotics and scaling limits for Gaussian polytopes
• Mean width of random polytopes in a reasonably smooth convex body
• Diameter of the Minkowski compactum is approximately equal to n
• Regular simplices and Gaussian samples
• Gaussian polytopes: a cumulant-based approach
• Brownian limits, local limits and variance asymptotics for convex hulls in the ball
• Central limit theorems for Gaussian polytopes
• Central limit theorems for random polytopes
• Intrinsic volumes of inscribed random polytopes in smooth convex bodies
• Stochastic and Integral Geometry
• Convex Bodies The Brunn-MinkowskiTheory
• Gaussian polytopes: variances and limit theorems
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