On Finite Rank Deformations of Wigner Matrices

Abstract

We study the distribution of the outliers in the spectrum of finite rank deformations of Wigner random matrice under the assumption that the off-diagonal matrix entries have uniformly bounded fifth moment and the diagonal entries have uniformly bounded third moment. Using our recent results on the fluctuation of resolvent entries [31],[28], and ideas from [9], we extend results by M.Capitaine, C.Donati-Martin, and D.Féral [12], [13].

accepted for publication in Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques

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• Rigidity of Eigenvalues of Generalized Wigner Matrices
• Fluctuations of the extreme eigenvalues of finite rank deformations of random matrices
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Cited by in corpus (9)

• The outliers of a deformed Wigner matrix
• Subordination for the sum of two random matrices
• Eigenvalue spectra of asymmetric random matrices for multi-component neural networks
• The Isotropic Semicircle Law and Deformation of Wigner Matrices
• On the principal components of sample covariance matrices
• Low rank perturbations of large elliptic random matrices
• On Fluctuations of Matrix Entries of Regular Functions of Wigner Matrices with Non-Identically Distributed Entries
• On Finite Rank Deformations of Wigner Matrices II: Delocalized Perturbations
• On a class of H-selfadjont random matrices with one eigenvalue of nonpositive type