A free analogue of Hincin’s characterization of infinite divisibility

Bercovici, Hari; Pata, Vittorino

doi:10.1090/S0002-9939-99-05087-X

A free analogue of Hincin’s characterization of infinite divisibility
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by Hari Bercovici and Vittorino Pata PDF

Proc. Amer. Math. Soc. 128 (2000), 1011-1015 Request permission

Abstract:

Hinčin 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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