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arXiv · 0706.0323

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

N. Raj Rao·Roland Speicher
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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.

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BibTeXRIS

N. Raj Rao, Roland Speicher. 2007-06-04. Multiplication of free random variables and the S-transform: the case of vanishing mean. https://arxiv.org/abs/0706.0323

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