Multiplication of free random variables and the S-transform: the case of vanishing mean
classification
🧮 math.OA
cs.ITmath.ITmath.PR
keywords
casemeans-transformfreevanishinganalyticalconvolutionextends
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This note extends Voiculescu's S-transform based analytical machinery for free multiplicative convolution to the case where the mean of the probability measures vanishes. We show that with the right interpretation of the S-transform in the case of vanishing mean, the usual formula makes perfectly good sense.
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