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

DOI:
https://doi.org/10.1090/S0002-9939-99-05087-X

Published electronically:
July 28, 1999

MathSciNet review:
1636930

Full-text PDF Free Access

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:
https://doi.org/10.1090/S0002-9939-99-05087-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