Sets of independent vectors in spaces of unlimitedly growing dimensionality

Abstract

We study a region of a space in which are concentrated independent observations of random vectors if the dimension of the space and the number of observations approaches infinity, and the distribution function of the components ξ_kⁱ of the observed vectors does not depend on n or m and satisfies the conditions: 1) it is continuous and symmetric: F (х) = 1 — F (—x); 2) its tails are slowly varying functions.