Multiplication of free random variables and the S-transform: the case of vanishing mean

Details Multiplication of free random variables and the S-transform: the case of vanishing mean Multiplication of free random variables and the S-transform: the case of vanishing mean

2007-06-04

arxiv.org/abs/0706.0323v1

Mathematics

Operator Algebras

Submitted to the Electronic Communications on Probability

Scientific paper

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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