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Limit Theorems for Additive Conditionally Free Convolution

Published online by Cambridge University Press:  20 November 2018

Jiun-Chau Wang
Jiun-Chau Wang*
Affiliation:
Department of Mathematics and Statistics, University of Saskatchewan, Saskatoon, SK, S7N 5E6freeprobability@gmail.com
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Abstract

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In this paper we determine the limiting distributional behavior for sums of infinitesimal conditionally free random variables. We show that the weak convergence of classical convolution and that of conditionally free convolution are equivalent for measures in an infinitesimal triangular array, where the measures may have unbounded support. Moreover, we use these limit theorems to study the conditionally free infinite divisibility. These results are obtained by complex analytic methods without reference to the combinatorics of $\text{c}$-free convolution.

Keywords

46L5360F05additive c-free convolutionlimit theoremsinfinitesimal arrays
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 63 , Issue 1 , 01 February 2011 , pp. 222 - 240
Copyright
Copyright © Canadian Mathematical Society 2011

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