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A Matrix Representation of the Bercovici-Pata Bijection


 
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1. Title Title of document A Matrix Representation of the Bercovici-Pata Bijection
 
2. Creator Author's name, affiliation, country Thierry Cabanal-Duvillard; Université Paris 5
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Random matrices, free probability, infinitely divisible laws
 
3. Subject Subject classification 15A52; 46L54; 60G51
 
4. Description Abstract Let $\mu$ be an infinitely divisible law on the real line, $\Lambda(\mu)$ its freely infinitely divisible image by the Bercovici-Pata bijection. The purpose of this article is to produce a new kind of random matrices with distribution $\mu$ at dimension 1, and with its empirical spectral law converging to $\Lambda(\mu)$ as the dimension tends to infinity. This constitutes a generalisation of Wigner's result for the Gaussian Unitary Ensemble.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2005-06-13
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/246
 
10. Identifier Digital Object Identifier 10.1214/EJP.v10-246
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 10
 
12. Language English=en
 
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