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Let X = ε 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.doi:10.1214/aop/1176989010 fatcat:ifex2n4xsjdahgng7rxgv5st7a