Multiplication of free random variables and the S-transform: the case of vanishing mean
نویسندگان
چکیده
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.
منابع مشابه
Hopf algebras and the logarithm of the S-transform in free probability – Extended abstract
Two basic tools of free probability are the R-transform and the S-transform. These transforms were introduced by Voiculescu in the 1980s, and are used to understand the addition and the multiplication of two free random variables respectively. The R-transform has a natural and very useful multi-variable extension describing the addition of two free k-tuples of random variables, but the problem ...
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ورودعنوان ژورنال:
- CoRR
دوره abs/0706.0323 شماره
صفحات -
تاریخ انتشار 2007