Electronic Journal of Probability

Low rank perturbations of large elliptic random matrices

Sean O'Rourke and David Renfrew

Full-text: Open access

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.  <br />

Article information

Source
Electron. J. Probab., Volume 19 (2014), paper no. 43, 65 pp.

Dates
Accepted: 4 May 2014
First available in Project Euclid: 4 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1465065685

Digital Object Identifier
doi:10.1214/EJP.v19-3057

Mathematical Reviews number (MathSciNet)
MR3210544

Zentralblatt MATH identifier
1315.60008

Subjects
Primary: 60B20: Random matrices (probabilistic aspects; for algebraic aspects see 15B52)

Keywords
elliptic random matrix low rank perturbation Wigner matrix

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

O'Rourke, Sean; Renfrew, David. Low rank perturbations of large elliptic random matrices. Electron. J. Probab. 19 (2014), paper no. 43, 65 pp. doi:10.1214/EJP.v19-3057. https://projecteuclid.org/euclid.ejp/1465065685


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