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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Limit theorems for free multiplicative convolutions


Authors: Hari Bercovici and Jiun-Chau Wang
Journal: Trans. Amer. Math. Soc. 360 (2008), 6089-6102
MSC (2000): Primary 46L54; Secondary 60F05
Published electronically: April 25, 2008
MathSciNet review: 2425704
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Abstract: We determine the distributional behavior for products of free random variables in a general infinitesimal triangular array. The main theorems in this paper extend a result for measures supported on the positive half-line, and provide a new limit theorem for measures on the unit circle with nonzero first moment.


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Additional Information

Hari Bercovici
Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405-4301
Email: bercovic@indiana.edu

Jiun-Chau Wang
Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405-4301
Email: jiuwang@indiana.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-08-04507-8
PII: S 0002-9947(08)04507-8
Received by editor(s): December 20, 2006
Published electronically: April 25, 2008
Additional Notes: The first author was supported in part by a grant from the National Science Foundation.
Article copyright: © Copyright 2008 American Mathematical Society