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Hin\v cin's Theorem for Multiplicative Free Convolution

Published:2008-03-01
Printed: Mar 2008
• S. T. Belinschi
• H. Bercovici
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Abstract

Hin\v cin proved that any limit law, associated with a triangular array of infinitesimal random variables, is infinitely divisible. The analogous result for additive free convolution was proved earlier by Bercovici and Pata. In this paper we will prove corresponding results for the multiplicative free convolution of measures definded on the unit circle and on the positive half-line.
 MSC Classifications: 46L53 - Noncommutative probability and statistics 60E07 - Infinitely divisible distributions; stable distributions 60E10 - Characteristic functions; other transforms

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