Outliers in spectrum of sparse Wigner matrices

DOI10.1002/rsa.20982zbMath1523.60019arXiv1904.07985MaRDI QIDQ6050001

Konstantin Tikhomirov, Pierre Youssef

Publication date: 11 October 2023

Published in: Random Structures & Algorithms (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1904.07985

zbMATH Keywords

outliersspectral gapmoment methodBBP phase transitionErdős-Rényi graph

Mathematics Subject Classification ID

Random graphs (graph-theoretic aspects) (05C80) Random matrices (probabilistic aspects) (60B20) Eigenvalues, singular values, and eigenvectors (15A18) Random matrices (algebraic aspects) (15B52)

Related Items

Local Marchenko-Pastur law for sparse rectangular random matrices ⋮ Bernoulli random matrices ⋮ Localized phase for the Erdős-Rényi graph ⋮ Finite rank perturbations of heavy-tailed Wigner matrices ⋮ Delocalization transition for critical Erdős-Rényi graphs ⋮ The completely delocalized region of the Erdős-Rényi graph ⋮ Poisson statistics and localization at the spectral edge of sparse Erdős-Rényi graphs

Cites Work

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• Outliers in the single ring theorem
• Spectral statistics of Erdős-Rényi graphs. I: Local semicircle law
• 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
• The outliers of a deformed Wigner matrix
• The eigenvalues and eigenvectors of finite, low rank perturbations of large random matrices
• Spectral statistics of Erdős-Rényi graphs II: eigenvalue spacing and the extreme eigenvalues
• On the distribution of the roots of certain symmetric matrices
• The largest eigenvalue of small rank perturbations of Hermitian random matrices
• The largest eigenvalues of finite rank deformation of large Wigner matrices: Convergence and nonuniversality of the fluctuations
• Limiting behavior of the norm of products of random matrices and two problems of Geman-Hwang
• The spectral radius of large random matrices
• The eigenvalues of random symmetric matrices
• The dimension-free structure of nonhomogeneous random matrices
• Local law and Tracy-Widom limit for sparse random matrices
• Norms of random matrices: local and global problems
• Complex outliers of Hermitian random matrices
• A proof of the block model threshold conjecture
• Concentration of measure and isoperimetric inequalities in product spaces
• On finite rank deformations of Wigner matrices
• Spectra of nearly Hermitian random matrices
• Central limit theorems for eigenvalues of deformations of Wigner matrices
• The largest eigenvalue of rank one deformation of large Wigner matrices
• Eigenvalues of large sample covariance matrices of spiked population models
• Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices
• Sparse random matrices: spectral edge and statistics of rooted trees
• Outlier Eigenvalues for Deformed I.I.D. Random Matrices
• The Isotropic Semicircle Law and Deformation of Wigner Matrices
• Handbook of Graph Theory
• A chaos hypothesis for some large systems of random equations
• The Expected Norm of Random Matrices
• High-Dimensional Probability
• Paths in graphs
• The Largest Eigenvalue of Sparse Random Graphs
• 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
• Spectral techniques applied to sparse random graphs
• Concentration and regularization of random graphs
• Spectral norm of random matrices