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2011 Kanter random variable and positive free stable distributions
Nizar Demni
Author Affiliations +
Electron. Commun. Probab. 16: 137-149 (2011). DOI: 10.1214/ECP.v16-1608


According to a representation due to M. Kanter, the density of some power of a positive stable distribution is a completely monotone function. In this paper, we first derive its representative Bernstein measure which also describes the law of some function of a uniform random variable, referred to below as the Kanter random variable. Then, the distribution function of the latter variable is written down and gives a more explicit description of the non commutative analogue of positive stable distributions in the setting of Voiculescu's free probability theory. Analytic evidences of the occurrence of the Kanter random variable in both the classical and the free settings conclude the exposition.


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Nizar Demni. "Kanter random variable and positive free stable distributions." Electron. Commun. Probab. 16 137 - 149, 2011.


Accepted: 17 March 2011; Published: 2011
First available in Project Euclid: 7 June 2016

zbMATH: 1225.60029
MathSciNet: MR2783335
Digital Object Identifier: 10.1214/ECP.v16-1608

Primary: 60E07
Secondary: 33E12, 60B20


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