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

N. Raj Rao, Roland Speicher

Type: Article

Publication Date: 2007-01-01

Citations: 41

DOI: https://doi.org/10.1214/ecp.v12-1274

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.

Locations

arXiv (Cornell University) - View - PDF
CiteSeer X (The Pennsylvania State University) - View
Electronic Communications in Probability - View - PDF

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