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Low rank perturbations of large elliptic random matrices

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1.	Title	Title of document	Low rank perturbations of large elliptic random matrices
2.	Creator	Author's name, affiliation, country	Sean O'Rourke; Yale University
2.	Creator	Author's name, affiliation, country	David Renfrew; UCLA
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	elliptic random matrix; low rank perturbation; Wigner matrix
3.	Subject	Subject classification	60B20
4.	Description	Abstract	We study the asymptotic behavior of outliers in the spectrum of bounded rank perturbations of large random matrices. In particular, we consider perturbations of elliptic random matrices which generalize both Wigner random matrices and non-Hermitian random matrices with iid entries. As a consequence, we recover the results of Capitaine, Donati-Martin, and Féral for perturbed Wigner matrices as well as the results of Tao for perturbed random matrices with iid entries.  Along the way, we prove a number of interesting results concerning elliptic random matrices whose entries have finite fourth moment; these results include a bound on the least singular value and the asymptotic behavior of the spectral radius.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2014-05-04
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/3057
10.	Identifier	Digital Object Identifier	10.1214/EJP.v19-3057
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 19
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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