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Kanter random variable and positive free stable distributions


 
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1. Title Title of document Kanter random variable and positive free stable distributions
 
2. Creator Author's name, affiliation, country Nizar Demni; Rennes 1 University
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Stable laws, free probability, Fox H-function
 
3. Subject Subject classification 60E07; 33E12; 60B20
 
4. Description Abstract 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) Research supported by CMCU 07G1501
 
7. Date (YYYY-MM-DD) 2011-03-17
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/1608
 
10. Identifier Digital Object Identifier 10.1214/ECP.v16-1608
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 16
 
12. Language English=en
 
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