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Hinčin's Theorem for Multiplicative Free Convolution

Published online by Cambridge University Press:  20 November 2018

S. T. Belinschi  and
H. Bercovici
S. T. Belinschi
Affiliation:
Department of Pure Mathematics, University of Waterloo, Waterloo, ON, N2L 3G1 e-mail: sbelinsc@math.uwaterloo.ca
H. Bercovici
Affiliation:
Department of Mathematics, University of Indiana, Bloomington, IN 47405-7000, U.S.A. e-mail: bercovic@indiana.edu
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Abstract

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Hinčin 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 defined on the unit circle and on the positive half-line.

Keywords

46L5360E0760E10
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 51 , Issue 1 , 01 March 2008 , pp. 26 - 31
Copyright
Copyright © Canadian Mathematical Society 2008

References

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