CLT and the volume of intersections of \(\ell_p^n\)-balls

DOI10.1023/A:1010353121014zbMath0988.52008OpenAlexW45223440MaRDI QIDQ5946247

Michael Schmuckenschlaeger

Publication date: 22 July 2002

Published in: Geometriae Dedicata (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1023/a:1010353121014

zbMATH Keywords

volumecentral limit theoremunit ball\(\ell^n_p\)-ball

Mathematics Subject Classification ID

Convexity and finite-dimensional Banach spaces (including special norms, zonoids, etc.) (aspects of convex geometry) (52A21) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Related Items (16)

Spectral flatness and the volume of intersections of \(p\)-ellipsoids ⋮ Projections of the uniform distribution on the cube: a large deviation perspective ⋮ A note about the uniform distribution on the intersection of a simplex and a sphere ⋮ Geometric sharp large deviations for random projections of \(\ell_p^n\) spheres and balls ⋮ Intersection of unit balls in classical matrix ensembles ⋮ Large deviations, moderate deviations, and the KLS conjecture ⋮ High-dimensional limit theorems for random vectors in ℓpn-balls ⋮ High-dimensional limit theorems for random vectors in ℓpn-balls. II ⋮ Sharp asymptotics for \(q\)-norms of random vectors in high-dimensional \(\ell_p^n\)-balls ⋮ Thin-shell concentration for random vectors in Orlicz balls via moderate deviations and Gibbs measures ⋮ The maximum entropy principle and volumetric properties of Orlicz balls ⋮ A new look at random projections of the cube and general product measures ⋮ Thin-shell theory for rotationally invariant random simplices ⋮ Exact asymptotic volume and volume ratio of Schatten unit balls ⋮ The surface measure and cone measure on the sphere of ℓ_{𝑝}ⁿ ⋮ Limit theorems for random points in a simplex

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