Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 16 (2011), paper no. 14, 137-149.
Kanter random variable and positive free stable distributions
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.
Electron. Commun. Probab., Volume 16 (2011), paper no. 14, 137-149.
Accepted: 17 March 2011
First available in Project Euclid: 7 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60E07: Infinitely divisible distributions; stable distributions
Secondary: 33E12: Mittag-Leffler functions and generalizations 60B20: Random matrices (probabilistic aspects; for algebraic aspects see 15B52)
This work is licensed under aCreative Commons Attribution 3.0 License.
Demni, Nizar. Kanter random variable and positive free stable distributions. Electron. Commun. Probab. 16 (2011), paper no. 14, 137--149. doi:10.1214/ECP.v16-1608. https://projecteuclid.org/euclid.ecp/1465261970