A probabilistic approach to the geometry of the \(\ell^n_p\)-ball
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Publication:1775438
DOI10.1214/009117904000000874zbMATH Open1071.60010arXivmath/0503650OpenAlexW1972194652MaRDI QIDQ1775438
Author name not available (Why is that?)
Publication date: 3 May 2005
Published in: (Search for Journal in Brave)
Abstract: This 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 psi_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.
Full work available at URL: https://arxiv.org/abs/math/0503650
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