Electronic Journal of Probability

Low rank perturbations of large elliptic random matrices

Sean O'Rourke and David Renfrew

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

elliptic random matrix low rank perturbation Wigner matrix

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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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