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Fluctuations of the Extreme Eigenvalues of Finite Rank Deformations of Random Matrices

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Fluctuations of the Extreme Eigenvalues of Finite Rank Deformations of Random Matrices
2.	Creator	Author's name, affiliation, country	Florent Benaych-Georges; UPMC Université Paris 6; France
2.	Creator	Author's name, affiliation, country	Alice Guionnet; École Normale Supérieure de Lyon; France
2.	Creator	Author's name, affiliation, country	Mylène Maida; Université Paris-Sud; France
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	random matrices ; spiked models ; extreme eigenvalue statistics ; Gaussian fluctuations ; Tracy-Widom laws
3.	Subject	Subject classification	60B20 ; 60F05
4.	Description	Abstract	Consider a deterministic self-adjoint matrix $X_n$ with spectral measure converging to a compactly supported probability measure, the largest and smallest eigenvalues converging to the edges of the limiting measure. We perturb this matrix by adding a random finite rank matrix with delocalised eigenvectors and study the extreme eigenvalues of the deformed model. We give necessary conditions on the deterministic matrix $X_n$ so that the eigenvalues converging out of the bulk exhibit Gaussian fluctuations, whereas the eigenvalues sticking to the edges are very close to the eigenvalues of the non-perturbed model and fluctuate in the same scale. We generalize these results to the case when $X_n$ is random and get similar behavior when we deform some classical models such as Wigner or Wishart matrices with rather general entries or the so-called matrix models.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	ANR
7.	Date	(YYYY-MM-DD)	2011-08-31
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/929
10.	Identifier	Digital Object Identifier	10.1214/EJP.v16-929
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 16
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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