The distribution of vector-valued Rademacher series
classification
🧮 math.FA
keywords
distributionformularademacherseriesvector-valuedapplicationsapproximatecertain
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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.
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