Universality of covariance matrices

DOI10.1214/13-AAP939zbMath1296.15021arXiv1110.2501MaRDI QIDQ2454401

Natesh S. Pillai, Jun Yin

Publication date: 13 June 2014

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1110.2501

zbMATH Keywords

Stieltjes transformcovariance matrixuniversalityWishart matrixDyson Brownian motionTracy-Widom lawMarcenko-Pastur lawasymptotic distribution of the eigenvaluesextremal singular valueslocal statistics of eigenvalues

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Brownian motion (60J65) Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Eigenvalues, singular values, and eigenvectors (15A18) Random matrices (algebraic aspects) (15B52)

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Cites Work

• Unnamed Item
• Spectral statistics of Erdős-Rényi graphs. I: Local semicircle law
• Local circular law for random matrices
• Random covariance matrices: universality of local statistics of eigenvalues
• A comment on the Wigner-Dyson-Mehta bulk universality conjecture for Wigner matrices
• Tracy-Widom law for the extreme eigenvalues of sample correlation matrices
• Random matrices: universality of local eigenvalue statistics
• Universality of random matrices and local relaxation flow
• Universality for generalized Wigner matrices with Bernoulli distribution
• Rigidity of eigenvalues of generalized Wigner matrices
• Limit of the smallest eigenvalue of a large dimensional sample covariance matrix
• Edge universality of correlation matrices
• Spectral statistics of Erdős-Rényi graphs II: eigenvalue spacing and the extreme eigenvalues
• A universality result for the smallest eigenvalues of certain sample covariance matrices
• Random matrices: The distribution of the smallest singular values
• Multivariate analysis and Jacobi ensembles: largest eigenvalue, Tracy-Widom limits and rates of convergence
• Universality results for the largest eigenvalues of some sample covariance matrix ensembles
• 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
• The distribution and moments of the smallest eigenvalue of a random matrix of Wishart type
• A note on universality of the distribution of the largest eigenvalues in certain sample covariance matrices
• On the distribution of the largest eigenvalue in principal components analysis
• Rate of convergence in probability to the Marchenko-Pastur law
• Bulk universality for generalized Wigner matrices
• Explaining the single factor bias of arbitrage pricing models in finite samples
• Eigenvector distribution of Wigner matrices
• Random matrices: Universality of local eigenvalue statistics up to the edge
• The local relaxation flow approach to universality of the local statistics for random matrices
• Universality in the bulk of the spectrum for complex sample covariance matrices
• A necessary and sufficient condition for edge universality of Wigner matrices
• The Isotropic Semicircle Law and Deformation of Wigner Matrices
• RANDOM COVARIANCE MATRICES: UNIVERSALITY OF LOCAL STATISTICS OF EIGENVALUES UP TO THE EDGE
• Application of Random Matrix Theory to Multivariate Statistics
• Bulk universality for Wigner matrices
• Testing Hypotheses About the Number of Factors in Large Factor Models
• A Brownian-Motion Model for the Eigenvalues of a Random Matrix
• Local Marchenko-Pastur law at the hard edge of sample covariance matrices
• DISTRIBUTION OF EIGENVALUES FOR SOME SETS OF RANDOM MATRICES
• Universality of local eigenvalue statistics for some sample covariance matrices

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