Asymptotic shape of the convex hull of isotropic log-concave random vectors

DOI10.1016/j.aam.2016.01.004zbMath1336.52005arXiv1601.02252OpenAlexW2234360442MaRDI QIDQ256340

Antonis Tsolomitis, Labrini Hioni, Apostolos Giannopoulos

Publication date: 9 March 2016

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

Full work available at URL: https://arxiv.org/abs/1601.02252

zbMATH Keywords

projectiondiameterpolytopeisotropycovering numberquermaßintegral

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 (4)

On the isotropic constant of random polytopes ⋮ On the isotropic constant of random polytopes with vertices on an \(\ell_p\)-sphere ⋮ On the geometry of random convex sets between polytopes and zonotopes ⋮ Affine quermassintegrals of random polytopes

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Centroid bodies and the logarithmic Laplace transform - A unified approach
• Asymptotic shape of a random polytope in a convex body
• On the hyperplane conjecture for random convex sets
• Concentration of mass on convex bodies
• On convex perturbations with a bounded isotropic constant
• Small ball probability and Dvoretzky's Theorem
• Convex measures on locally convex spaces
• Blaschke-Santaló inequalities
• Global versus local asymptotic theories of finite-dimensional normed spaces
• Quermassintegrals of a random polytope in a convex body
• \(L_ p\) affine isoperimetric inequalities.
• Duality of metric entropy
• New volume ratio properties for convex symmetric bodies in \({\mathbb{R}}^ n\)
• Quermaßintegrals and asymptotic shape of random polytopes in an isotropic convex body
• A new approach to several results of V. Milman.
• On the isotropy constant of random convex sets
• Quantitative estimates of the convergence of the empirical covariance matrix in log-concave ensembles
• On mean outer radii of random polytopes
• Geometry of the 𝐿_{𝑞}-centroid bodies of an isotropic log-concave measure
• M-Estimates for Isotropic Convex Bodies and Their L q -Centroid Bodies
• On the Mean-Width of Isotropic Convex Bodies and their Associated Lp-Centroid Bodies
• Asymptotic Geometric Analysis, Part I
• Small ball probability estimates for log-concave measures
• Convex Bodies The Brunn-MinkowskiTheory
• On the Gaussian behavior of marginals and the mean width of random polytopes
• On the isotropic constant of random polytopes
• On the isotropic constant of random polytopes

This page was built for publication: Asymptotic shape of the convex hull of isotropic log-concave random vectors