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Large deviations for the largest eigenvalue of rank one deformations of Gaussian ensembles


 
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1. Title Title of document Large deviations for the largest eigenvalue of rank one deformations of Gaussian ensembles
 
2. Creator Author's name, affiliation, country Mylène Maida; Université Paris-Sud
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) large deviations ; random matrices
 
3. Subject Subject classification 60F10 ; 15A52
 
4. Description Abstract We establish a large deviation principle for the largest eigenvalue of a rank one deformation of a matrix from the GUE or GOE. As a corollary, we get another proof of the phenomenon, well-known in learning theory and finance, that the largest eigenvalue separates from the bulk when the perturbation is large enough. A large part of the paper is devoted to an auxiliary result on the continuity of spherical integrals in the case when one of the matrix is of rank one, as studied in one of our previous works.
 
5. Publisher Organizing agency, location
 
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7. Date (YYYY-MM-DD) 2007-08-25
 
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/438
 
10. Identifier Digital Object Identifier 10.1214/EJP.v12-438
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 12
 
12. Language English=en
 
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