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 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 functional 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 l-norm), and derive several monotonicity results as p varies. Applications to balancing vectors in l 2 and to covering numbers of polyhedra complete the exposition.
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty
- Extremal sections
- Gaussian measure
- L -ball