Open Access
2014 Low rank perturbations of large elliptic random matrices
Sean O'Rourke, David Renfrew
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Electron. J. Probab. 19: 1-65 (2014). DOI: 10.1214/EJP.v19-3057


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 />


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Sean O'Rourke. David Renfrew. "Low rank perturbations of large elliptic random matrices." Electron. J. Probab. 19 1 - 65, 2014.


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

zbMATH: 1315.60008
MathSciNet: MR3210544
Digital Object Identifier: 10.1214/EJP.v19-3057

Primary: 60B20

Keywords: elliptic random matrix , low rank perturbation , Wigner matrix

Vol.19 • 2014
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