On the Gaussian behavior of marginals and the mean width of random polytopes

DOI10.1090/S0002-9939-2014-12401-4zbMath1310.52006arXiv1205.6174OpenAlexW2086743286MaRDI QIDQ5496322

David Alonso-Gutiérrez, Joscha Prochno

Publication date: 30 January 2015

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1205.6174

zbMATH Keywords

random polytopeOrlicz normmean widthsubgaussian directionsupergaussian direction

Mathematics Subject Classification ID

Probabilistic methods in Banach space theory (46B09) Random convex sets and integral geometry (aspects of convex geometry) (52A22) Probabilistic methods in extremal combinatorics, including polynomial methods (combinatorial Nullstellensatz, etc.) (05D40) Asymptotic theory of convex bodies (52A23)

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Quermaßintegrals and asymptotic shape of random polytopes in an isotropic convex body ⋮ Mean width of random perturbations of random polytopes ⋮ Thin-shell concentration for random vectors in Orlicz balls via moderate deviations and Gibbs measures ⋮ On the geometry of random convex sets between polytopes and zonotopes ⋮ Probabilistic estimates for tensor products of random vectors ⋮ Asymptotic shape of the convex hull of isotropic log-concave random vectors

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