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

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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

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