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May 2011 A continuous semigroup of notions of independence between the classical and the free one
Florent Benaych-Georges, Thierry Lévy
Ann. Probab. 39(3): 904-938 (May 2011). DOI: 10.1214/10-AOP573

Abstract

In this paper, we investigate a continuous family of notions of independence which interpolates between the classical and free ones for noncommutative random variables. These notions are related to the liberation process introduced by Voiculescu. To each notion of independence correspond new convolutions of probability measures, for which we establish formulae and of which we compute simple examples. We prove that there exists no reasonable analogue of classical and free cumulants associated to these notions of independence.

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Florent Benaych-Georges. Thierry Lévy. "A continuous semigroup of notions of independence between the classical and the free one." Ann. Probab. 39 (3) 904 - 938, May 2011. https://doi.org/10.1214/10-AOP573

Information

Published: May 2011
First available in Project Euclid: 16 March 2011

zbMATH: 1222.46049
MathSciNet: MR2789579
Digital Object Identifier: 10.1214/10-AOP573

Subjects:
Primary: 15A52 , 46L54

Keywords: convolution , Cumulants , Free probability , independence , random matrices , unitary Brownian motion

Rights: Copyright © 2011 Institute of Mathematical Statistics

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Vol.39 • No. 3 • May 2011
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