### The Distribution of Vector-Valued Rademacher Series

S. J. Dilworth and S. J. Montgomery-Smith
Source: Ann. Probab. Volume 21, Number 4 (1993), 2046-2052.

#### Abstract

Let $X = \sum\varepsilon_nx_n$ 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.

First Page:
Primary Subjects: 46B20
Secondary Subjects: 60B11, 60G50
Full-text: Open access