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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A free analogue of Hincin's characterization
of infinite divisibility


Authors: Hari Bercovici and Vittorino Pata
Journal: Proc. Amer. Math. Soc. 128 (2000), 1011-1015
MSC (1991): Primary 46L50, 60E07; Secondary 60E10
Published electronically: July 28, 1999
MathSciNet review: 1636930
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Abstract | References | Similar Articles | Additional Information

Abstract: Hincin characterized the class of infinitely divisible distributions on the line as the class of all distributional limits of sums of infinitesimal independent random variables. We show that an analogue of this characterization is true in the addition theory of free random variables introduced by Voiculescu.


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Additional Information

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

Vittorino Pata
Affiliation: Dipartimento di Matematica, Università di Brescia, Brescia 25123, Italy
Email: pata@ing.unibs.it

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05087-X
PII: S 0002-9939(99)05087-X
Received by editor(s): May 13, 1998
Published electronically: July 28, 1999
Additional Notes: The first author was partially supported by a grant from the National Science Foundation.
Communicated by: Dale Alspach
Article copyright: © Copyright 2000 American Mathematical Society