Uniform in dimension estimates of the scatter of distributions of Gaussian random functionals for some classes of multivariate measures

We establish uniform in dimension estimates of the scatter of distributions of linear functionals chosen at random with respect to the Gaussian distribution for uniform discrete distributions and for Gaussian distributions on a vector space. Bibliography: 5 titles.Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 294, 2002, pp. 194–199.This research was supported by the Russian Foundation for Basic Research, grants 99-15-96019, 02-01-00263, and 99-01-04027.Translated by V. N. Sudakov.