Canadian Mathematical Society www.cms.math.ca
Abstract view

# Limit Theorems for Additive Conditionally Free Convolution

Published:2010-09-30
Printed: Feb 2011
• Jiun-Chau Wang,
Department of Mathematics and Statistics, University of Saskatchewan, Saskatoon, SK, S7N 5E6
Features coming soon:
Citations   (via CrossRef) Tools: Search Google Scholar:
 Format: HTML LaTeX MathJax PDF

## Abstract

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 c-free convolution.
 Keywords: additive c-free convolution, limit theorems, infinitesimal arrays
 MSC Classifications: 46L53 - Noncommutative probability and statistics 60F05 - Central limit and other weak theorems

© Canadian Mathematical Society, 2013 : http://www.cms.math.ca/