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Fixed Points of the Smoothing Transform:the Boundary Case
Fixed Points Smoothing Boundary Case
2009/4/8
Let $A=(A_1,A_2,A_3,ldots)$ be a random sequence of non-negative numbers that are ultimately zero with $E[sum A_i]=1$ and $E left[sum A_{i} log A_i right] leq 0$. The uniqueness of the non-negative fi...
Multiplication of free random variables and the S-transform:the case of vanishing mean
free random variable S-transform vanishing mean
2009/3/27
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 i...