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

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