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Limit Theorems for Additive Conditionally Free Convolution
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- Journal:
- Canadian Journal of Mathematics / Volume 63 / Issue 1 / 01 February 2011
- Published online by Cambridge University Press:
- 20 November 2018, pp. 222-240
- Print publication:
- 01 February 2011
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- Article
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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.
