Mean width of random polytopes in a reasonably smooth convex body

DOI10.1016/j.jmva.2009.07.003zbMath1221.52008OpenAlexW2069892885MaRDI QIDQ1036792

Károly jun. Böröczky, Ferenc Fodor, Matthias Reitzner, Viktor Vígh

Publication date: 13 November 2009

Published in: Journal of Multivariate Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmva.2009.07.003

zbMATH Keywords

random polytopemean width

Mathematics Subject Classification ID

Random convex sets and integral geometry (aspects of convex geometry) (52A22)

Related Items

THE VOLUME OF RANDOM POLYTOPES CIRCUMSCRIBED AROUND A CONVEX BODY ⋮ Variance bounds for disc-polygons ⋮ On Random Disc Polygons in Smooth Convex Discs ⋮ Uniform behaviors of random polytopes under the Hausdorff metric ⋮ Variance estimates for random disc-polygons in smooth convex discs ⋮ Asymptotic normality for random polytopes in non-Euclidean geometries ⋮ Intrinsic volumes and Gaussian polytopes: the missing piece of the jigsaw ⋮ Intrinsic volumes of inscribed random polytopes in smooth convex bodies ⋮ Limit theorems for random polytopes with vertices on convex surfaces ⋮ Expectation of intrinsic volumes of random polytopes

Cites Work

• Central limit theorems for random polytopes in a smooth convex set
• Approximation of convex bodies by random polytopes
• Random polytopes in a convex polytope, independence of shape, and concentration of vertices
• Approximation of smooth convex bodies by random circumscribed polytopes
• Random polytopes and the Efron-Stein jackknife inequality.
• An identity relating moments of functionals of convex hulls
• Central limit theorems for random polytopes
• Stochastic and Integral Geometry
• Convex bodies, economic cap coverings, random polytopes
• Random polytopes in smooth convex bodies
• Random polytopes in a convex body
• Random Polytopes and Affine Surface Area
• Convex and Discrete Geometry
• [https://portal.mardi4nfdi.de/wiki/Publication:5331598 �ber die konvexe H�lle von n zuf�llig gew�hlten Punkten. II]
• ZufÄllige konvexe Polygone in einem Ringgebiet
• [https://portal.mardi4nfdi.de/wiki/Publication:5728818 �ber die konvexe H�lle von n zuf�llig gew�hlten Punkten]
• Expectation of random polytopes
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item