Proportional concentration phenomena on the sphere

DOI10.1007/BF02784520zbMath1027.46011OpenAlexW2094492505WikidataQ56050912 ScholiaQ56050912MaRDI QIDQ1860714

Shiri Artstein-Avidan

Publication date: 13 January 2004

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02784520

zbMATH Keywords

entropy numbersconcentration phenomenon

Mathematics Subject Classification ID

Local theory of Banach spaces (46B07) Riesz operators; eigenvalue distributions; approximation numbers, (s)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators (47B06) Probabilistic methods in Banach space theory (46B09) Convexity and finite-dimensional Banach spaces (including special norms, zonoids, etc.) (aspects of convex geometry) (52A21)

Related Items (11)

High-dimensional tennis balls ⋮ More on the duality conjecture for entropy numbers. ⋮ Duality of metric entropy in Euclidean space. ⋮ On the isotropic constant of random polytopes ⋮ A Bernstein-Chernoff deviation inequality, and geometric properties of random families of operators ⋮ Asymptotic formulas for the diameter of sections of symmetric convex bodies ⋮ Isoperimetry of waists and local versus global asymptotic convex geometries ⋮ Approximation with random bases: pro et contra ⋮ Impossibility of dimension reduction in the nuclear norm ⋮ From Steiner formulas for cones to concentration of intrinsic volumes ⋮ Exponential and Gaussian concentration of 1-Lipschitz maps

Cites Work

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• Asymptotic theory of finite dimensional normed spaces. With an appendix by M. Gromov: Isoperimetric inequalities in Riemannian manifolds
• A dozen de Finetti-style results in search of a theory
• Entropy and asymptotic geometry of non-symmetric convex bodies
• A new approach to several results of V. Milman.
• Extensions of Lipschitz mappings into a Hilbert space
• Subspaces of Small Codimension of Finite-Dimensional Banach Spaces
• A normal approximation for beta and gamma tail probabilities

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