Some strong convergence theorems for eigenvalues of general sample covariance matrices

DOI10.1142/S2010326322500290zbMath1493.15118OpenAlexW3216084710WikidataQ113775125 ScholiaQ113775125MaRDI QIDQ5092963

Yanqing Yin

Publication date: 26 July 2022

Published in: Random Matrices: Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s2010326322500290

zbMATH Keywords

largest eigenvalueextreme eigenvaluesspectral normsample covariance matricesspectrum separation

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Strong limit theorems (60F15) Random matrices (algebraic aspects) (15B52)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The limit of the smallest singular value of random matrices with i.i.d. entries
• Limit of the smallest eigenvalue of a large dimensional sample covariance matrix
• No eigenvalues outside the support of the limiting empirical spectral distribution of a separable covariance matrix
• A universality result for the smallest eigenvalues of certain sample covariance matrices
• Universality results for the largest eigenvalues of some sample covariance matrix ensembles
• Spectral analysis of large dimensional random matrices
• On the limit of the largest eigenvalue of the large dimensional sample covariance matrix
• A note on the largest eigenvalue of a large dimensional sample covariance matrix
• Some limit theorems for the eigenvalues of a sample covariance matrix
• Distribution function inequalities for martingales
• The strong limits of random matrix spectra for sample matrices of independent elements
• No eigenvalues outside the support of the limiting spectral distribution of large-dimensional sample covariance matrices
• Exact separation of eigenvalues of large dimensional sample covariance matrices
• A necessary and sufficient condition for edge universality at the largest singular values of covariance matrices
• On the empirical distribution of eigenvalues of a class of large dimensional random matrices
• Strong convergence of the empirical distribution of eigenvalues of large dimensional random matrices
• CLT for linear spectral statistics of large dimensional sample covariance matrices with dependent data
• On the convergence of the extremal eigenvalues of empirical covariance matrices with dependence
• The Tracy-Widom limit for the largest eigenvalues of singular complex Wishart matrices
• Limit theory for the largest eigenvalues of sample covariance matrices with heavy-tails
• Universality of covariance matrices
• Matrix Analysis
• On Structure Testing for Component Covariance Matrices of a High Dimensional Mixture
• Joint Central Limit Theorem for Eigenvalue Statistics from Several Dependent Large Dimensional Sample Covariance Matrices with Application

This page was built for publication: Some strong convergence theorems for eigenvalues of general sample covariance matrices