Multiplication of free random variables and the S-transform: the case of vanishing mean
arXiv:0706.0323
Abstract
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.
Submitted to the Electronic Communications on Probability