On the isotropic constant of random polytopes

DOI10.1515/ADVGEOM.2010.009zbMath1208.52004MaRDI QIDQ5900883

Apostolos Giannopoulos, N. Dafnis, Olivier Guédon

Publication date: 6 May 2010

Published in: advg (Search for Journal in Brave)

zbMATH Keywords

random pointsisotropic constantinertia matrixunconditional 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 (12)

ON THE EXISTENCE OF SUPERGAUSSIAN DIRECTIONS ON CONVEX BODIES ⋮ Gaussian polytopes: a cumulant-based approach ⋮ On the isotropy constant of projections of polytopes ⋮ Facets of spherical random polytopes ⋮ Estimating support functions of random polytopes via Orlicz norms ⋮ On the isotropic constant of random polytopes ⋮ Poincaré inequality in mean value for Gaussian polytopes ⋮ On the isotropic constant of random polytopes with vertices on an \(\ell_p\)-sphere ⋮ The isotropic constant of random polytopes with vertices on convex surfaces ⋮ Asymptotic shape of a random polytope in a convex body ⋮ Poisson polyhedra in high dimensions ⋮ Asymptotic shape of the convex hull of isotropic log-concave random vectors

Cites Work

• On the hyperplane conjecture for random convex sets
• Concentration of mass on convex bodies
• On convex perturbations with a bounded isotropic constant
• A probabilistic approach to the geometry of the \(\ell^n_p\)-ball
• Proportional concentration phenomena on the sphere
• On the isotropy constant of random convex sets
• Volume radius of a random polytope in a convex body
• Concentration property on probability spaces.

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