Asymptotic Theory of Eigenvectors for Random Matrices With Diverging Spikes

DOI10.1080/01621459.2020.1840990OpenAlexW3094036661MaRDI QIDQ5885123

No author found.

Publication date: 27 March 2023

Published in: Journal of the American Statistical Association (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1902.06846

zbMATH Keywords

eigenvectorshigh dimensionalityasymptotic distributionsrandom matrix theorylow-rank matrixgeneralized Wigner matrix

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20)

Related Items (5)

Eigen Selection in Spectral Clustering: A Theory-Guided Practice ⋮ Universal rank inference via residual subsampling with application to large networks ⋮ Entrywise limit theorems for eigenvectors of signal-plus-noise matrix models with weak signals ⋮ Mixed Membership Estimation for Social Networks ⋮ Using SVD for Topic Modeling

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Network cross-validation by edge sampling
• Network Cross-Validation for Determining the Number of Communities in Network Data
• Delocalization and diffusion profile for random band matrices
• The outliers of a deformed Wigner matrix
• Asymptotics and concentration bounds for bilinear forms of spectral projectors of sample covariance
• The eigenvector moment flow and local quantum unique ergodicity
• Spectral clustering and the high-dimensional stochastic blockmodel
• Rigidity of eigenvalues of generalized Wigner matrices
• Anisotropic local laws for random matrices
• No-gaps delocalization for general random matrices
• Central limit theorems for eigenvalues in a spiked population model
• Characteristic vectors of bordered matrices with infinite dimensions
• Spectral partitioning works: planar graphs and finite element meshes
• Controlling the false discovery rate via knockoffs
• Community detection in sparse random networks
• Multivariate analysis and Jacobi ensembles: largest eigenvalue, Tracy-Widom limits and rates of convergence
• The eigenvalues of random symmetric matrices
• Level-spacing distributions and the Airy kernel
• Limit theorems for eigenvectors of the normalized Laplacian for random graphs
• On the distribution of the largest eigenvalue in principal components analysis
• On orthogonal and symplectic matrix ensembles
• On finite rank deformations of Wigner matrices
• Asymptotics of empirical eigenstructure for high dimensional spiked covariance
• Entrywise eigenvector analysis of random matrices with low expected rank
• Tracy-Widom limit for the largest eigenvalue of a large class of complex sample covariance matrices
• Central limit theorems for eigenvalues of deformations of Wigner matrices
• Community detection in dense random networks
• On the asymptotic distribution of the eigenvalues of random matrices
• Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices
• Singular vector and singular subspace distribution for the matrix denoising model
• The Isotropic Semicircle Law and Deformation of Wigner Matrices
• A nonparametric view of network models and Newman–Girvan and other modularities
• Random Band Matrices in the Delocalized Phase I: Quantum Unique Ergodicity and Universality
• RANK: Large-Scale Inference With Graphical Nonlinear Knockoffs
• Community Detection and Stochastic Block Models
• An $\ell_{\infty}$ Eigenvector Perturbation Bound and Its Application to Robust Covariance Estimation
• A Simple SVD Algorithm for Finding Hidden Partitions
• ON FINITE RANK DEFORMATIONS OF WIGNER MATRICES II: DELOCALIZED PERTURBATIONS
• Panning for Gold: ‘Model-X’ Knockoffs for High Dimensional Controlled Variable Selection
• Detecting Overlapping Communities in Networks Using Spectral Methods
• Non universality of fluctuations of outlier eigenvectors for block diagonal deformations of Wigner matrices
• IPAD: Stable Interpretable Forecasting with Knockoffs Inference
• On Consistency and Sparsity for Principal Components Analysis in High Dimensions
• DISTRIBUTION OF EIGENVALUES FOR SOME SETS OF RANDOM MATRICES
• On Wigner's semicircle law for the eigenvalues of random matrices
• A goodness-of-fit test for stochastic block models

This page was built for publication: Asymptotic Theory of Eigenvectors for Random Matrices With Diverging Spikes