Cauchy-Stieltjes Kernel Families and Free Multiplicative Convolution

Abstract

In this paper, we determine the effect of the free multiplicative convolution on the pseudo-variance function of a Cauchy-Stieltjes kernel family. We then use the machinery of variance functions to establish some limit theorems related to this type of convolution and involving the free additive convolution and the Boolean additive convolution.

Keywords

Variance function / Cauchy kernel / Free multiplicative convolution / S-transform