Outlier Eigenvalues for Deformed I.I.D. Random Matrices

DOI10.1002/cpa.21629zbMath1353.15032arXiv1403.6001OpenAlexW2963740588MaRDI QIDQ2828466

Charles Bordenave, Mireille Capitaine

Publication date: 26 October 2016

Published in: Communications on Pure and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1403.6001

zbMATH Keywords

eigenvaluerandom matrixoutlieroutlier eigenvalue

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Eigenvalues, singular values, and eigenvectors (15A18) Random matrices (algebraic aspects) (15B52)

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Cites Work

• Unnamed Item
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• Outliers in the single ring theorem
• Gaussian fluctuations for linear spectral statistics of large random covariance matrices
• Erratum to: Outliers in the spectrum of iid matrices with bounded rank perturbations
• Fluctuations of the extreme eigenvalues of finite rank deformations of random matrices
• Free convolution with a semicircular distribution and eigenvalues of spiked deformations of Wigner matrices
• Almost sure localization of the eigenvalues in a Gaussian information plus noise model. Application to the spiked models.
• Around the circular law
• The singular values and vectors of low rank perturbations of large rectangular random matrices
• The outliers of a deformed Wigner matrix
• The eigenvalues and eigenvectors of finite, low rank perturbations of large random matrices
• On the spectrum of sum and product of non-Hermitian random matrices
• The single ring theorem
• Outliers in the spectrum of large deformed unitarily invariant models
• Limit of the smallest eigenvalue of a large dimensional sample covariance matrix
• On sample eigenvalues in a generalized spiked population model
• The largest eigenvalue of small rank perturbations of Hermitian random matrices
• Analysis of the limiting spectral distribution of large dimensional information-plus-noise type matrices
• The largest eigenvalues of finite rank deformation of large Wigner matrices: Convergence and nonuniversality of the fluctuations
• Spectral analysis of large dimensional random matrices
• The eigenvalues of random symmetric matrices
• Brown's spectral distribution measure for \(R\)-diagonal elements in finite von Neumann algebras
• Random regularization of Brown spectral measure
• Support convergence in the single ring theorem
• On finite rank deformations of Wigner matrices
• Random matrices: universality of ESDs and the circular law
• Low rank perturbations of large elliptic random matrices
• On the empirical distribution of eigenvalues of large dimensional information-plus-noise-type matrices
• Central limit theorems for eigenvalues of deformations of Wigner matrices
• Logarithmic Sobolev inequalities for mollified compactly supported measures
• Large deviations for the largest eigenvalue of rank one deformations of Gaussian ensembles
• The largest eigenvalue of rank one deformation of large Wigner matrices
• Zeros of the i.i.d. Gaussian power series: a conformally invariant determinantal process
• Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices
• Computation of some examples of Brown's spectral measure in free probability
• The Isotropic Semicircle Law and Deformation of Wigner Matrices
• NO EIGENVALUES OUTSIDE THE SUPPORT OF THE LIMITING SPECTRAL DISTRIBUTION OF INFORMATION-PLUS-NOISE TYPE MATRICES
• The Hadamard Operator Norm of a Circulant and Applications
• Regularization of Non-Normal Matrices by Gaussian Noise
• Random matrix theory
• Eigenvalue separation in some random matrix models
• An Introduction to Random Matrices
• How many zeros of a random polynomial are real?
• An Introduction to the Theory of Point Processes
• Asymptotic freeness by generalized moments for Gaussian and Wishart matrices. Application to beta random matrices
• ON FINITE RANK DEFORMATIONS OF WIGNER MATRICES II: DELOCALIZED PERTURBATIONS
• Exact separation phenomenon for the eigenvalues of large Information-Plus-Noise type matrices. Application to spiked models
• Universal sum and product rules for random matrices
• From the Littlewood-Offord problem to the Circular Law: Universality of the spectral distribution of random matrices
• Invertibility of random matrices: Unitary and orthogonal perturbations
• Spectrum of Markov Generators on Sparse Random Graphs
• Numerical inverting of matrices of high order
• Spectral norm of random matrices

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