A probabilistic approach to the geometry of the \ell_p^n-ball

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dc.creatorBarthe, Franck
dc.creatorGuedon, Olivier
dc.creatorMendelson, Shahar
dc.creatorNaor, Assaf
dc.date2005-03-29
dc.date.accessioned2026-07-07T05:18:34Z
dc.date.available2026-07-07T05:18:34Z
dc.descriptionThis article investigates, by probabilistic methods, various geometric questions on B_p^n, the unit ball of \ell_p^n. We propose realizations in terms of independent random variables of several distributions on B_p^n, including the normalized volume measure. These representations allow us to unify and extend the known results of the sub-independence of coordinate slabs in B_p^n. As another application, we compute moments of linear functionals on B_p^n, which gives sharp constants in Khinchine's inequalities on B_p^n and determines the ψ_2-constant of all directions on B_p^n. We also study the extremal values of several Gaussian averages on sections of B_p^n (including mean width and \ell-norm), and derive several monotonicity results as p varies. Applications to balancing vectors in \ell_2 and to covering numbers of polyhedra complete the exposition.
dc.descriptionPublished at http://dx.doi.org/10.1214/009117904000000874 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/math/0503650
dc.identifierhttp://arxiv.org/abs/math/0503650
dc.identifierAnnals of Probability 2005, Vol. 33, No. 2, 480-513
dc.identifierdoi:10.1214/009117904000000874
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/74706
dc.subjectProbability
dc.subject60E15, 52A20, 52A38, 52A40. (Primary)
dc.titleA probabilistic approach to the geometry of the \ell_p^n-ball
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