Quermaßintegrals and asymptotic shape of random polytopes in an isotropic convex body

DOI10.1307/mmj/1363958241zbMath1279.52010OpenAlexW2088597097MaRDI QIDQ1951493

N. Dafnis, Apostolos Giannopoulos, Antonis Tsolomitis

Publication date: 6 June 2013

Published in: Michigan Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.mmj/1363958241

zbMATH Keywords

random polytopequermassintegralisotropic convex body

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Local theory of Banach spaces (46B07) Inequalities and extremum problems involving convexity in convex geometry (52A40) Convexity and finite-dimensional Banach spaces (including special norms, zonoids, etc.) (aspects of convex geometry) (52A21) Random convex sets and integral geometry (aspects of convex geometry) (52A22)

Related Items (8)

Mean width of random perturbations of random polytopes ⋮ Estimating support functions of random polytopes via Orlicz norms ⋮ On the isotropic constant of random polytopes ⋮ On the geometry of random convex sets between polytopes and zonotopes ⋮ Gaussian convex bodies: a nonasymptotic approach ⋮ Affine quermassintegrals of random polytopes ⋮ On the Gaussian behavior of marginals and the mean width of random polytopes ⋮ Asymptotic shape of the convex hull of isotropic log-concave random vectors

Cites Work

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• Order statistics and concentration of \(l_r\) norms for log-concave vectors
• On determinants and the volume of random polytopes in isotropic convex bodies
• Centroid bodies and the logarithmic Laplace transform - A unified approach
• Asymptotic shape of a random polytope in a convex body
• \(L_{p}\)-moments of random vectors via majorizing measures
• Concentration of mass on convex bodies
• Small ball probability and Dvoretzky's Theorem
• On singular values of matrices with independent rows
• Asymptotic theory of finite dimensional normed spaces. With an appendix by M. Gromov: Isoperimetric inequalities in Riemannian manifolds
• Gelfand numbers of operators with values in a Hilbert space
• Averages of norms and quasi-norms
• \(L_ p\) affine isoperimetric inequalities.
• A probabilistic approach to the geometry of the \(\ell^n_p\)-ball
• Random spaces generated by vertices of the cube
• Isoperimetric problems for convex bodies and a localization lemma
• Smallest singular value of random matrices and geometry of random polytopes
• VaR modelling on long run horizons
• The geometry of random \(\{-1,1\}\)-polytopes
• Quantitative estimates of the convergence of the empirical covariance matrix in log-concave ensembles
• Logarithmically concave functions and sections of convex sets in $R^{n}$
• Approximation of the Sphere by Polytopes having Few Vertices
• Small ball probability estimates for log-concave measures
• Tail estimates for norms of sums of log-concave random vectors
• On the Gaussian behavior of marginals and the mean width of random polytopes

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