On Finite Rank Deformations of Wigner Matrices

2011/03/18 by Alessandro Pizzo, Pizzo, Alessandro, David Renfrew +3 · 2 citations
Mathematics · #60B20 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.1103.3731

openalex publication_date 2011/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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].

Citations

• Central Limit Theorem for linear eigenvalue statistics of the Wigner and sample covariance random matrices
• Fluctuations of the extreme eigenvalues of finite rank deformations of random matrices

Cited by

• Spectral statistics and energy-gap scaling in k-local spin Hamiltonians
• Monitoring for a Phase Transition in a Time Series of Wigner Matrices

Related

• On Finite Rank Deformations of Wigner Matrices II: Delocalized Perturbations
• The Isotropic Semicircle Law and Deformation of Wigner Matrices
• Non universality of fluctuations of outlier eigenvectors for block diagonal deformations of Wigner matrices
• Outliers for deformed inhomogeneous random matrices
• Finite rank perturbation of non-Hermitian random matrices: heavy tail and sparse regimes