The distribution of vector-valued Rademacher series

Stephen J. Dilworth, Stephen J. Montgomery-Smith

Published 1992-06-01, updated 1999-12-06Version 2

Let $X=\sum \epsilon_n x_n$ be a Rademacher series with vector-valued coefficients. We obtain an approximate formula for the distribution of the random variable $||X||$ in terms of its mean and a certain quantity derived from the K-functional of interpolation theory. Several applications of the formula are given.