A probabilistic approach to the geometry of the lnp-ball

• 成果类型: Article
• 署名作者: Barthe, F; Guédon, O; Mendelson, S; Naor, A
• 署名单位: Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite; Sorbonne Universite; Australian National University; Microsoft
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117904000000874
• 发表日期: 2005
• 页码: 480-513
• 关键词: unit ball; sections; volume; slabs; CUBE

摘要

This article investigates, by probabilistic methods, various geometric questions on B-p(n), the unit ball of l(p)(n). We propose realizations in terms of independent random variables of several distributions on B-p(n), including the P 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 l-norm), and derive several monotonicity results as varies. Applications to balancing vectors in l(2) and to covering numbers of polyhedra complete the exposition.