RANDOM COVARIANCE MATRICES: UNIVERSALITY OF LOCAL STATISTICS OF EIGENVALUES UP TO THE EDGE

DOI10.1142/S2010326311500055zbMath1288.15047arXiv1104.4832MaRDI QIDQ2893155

Ke Wang

Publication date: 26 June 2012

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

Full work available at URL: https://arxiv.org/abs/1104.4832

zbMATH Keywords

universalityrandom covariance matricesfour moment theorem

Mathematics Subject Classification ID

Multivariate analysis (62H99) Random matrices (probabilistic aspects) (60B20) Random matrices (algebraic aspects) (15B52)

Related Items (17)

The Tracy-Widom law for the largest eigenvalue of F type matrices ⋮ Random weighted projections, random quadratic forms and random eigenvectors ⋮ On delocalization of eigenvectors of random non-Hermitian matrices ⋮ Convergence rate to the Tracy-Widom laws for the largest eigenvalue of sample covariance matrices ⋮ Quantitative Tracy-Widom laws for the largest eigenvalue of generalized Wigner matrices ⋮ Local Marchenko–Pastur law at the hard edge of the sample covariance ensemble ⋮ Random matrix theory in statistics: a review ⋮ Universality of covariance matrices ⋮ Local Marchenko-Pastur law at the hard edge of sample covariance matrices ⋮ Fluctuations of the free energy of the spherical Sherrington-Kirkpatrick model ⋮ Large complex correlated Wishart matrices: fluctuations and asymptotic independence at the edges ⋮ Tracy-Widom limit for Kendall's tau ⋮ Eigenvectors of random matrices: A survey ⋮ Spectral Properties of Wigner Matrices ⋮ Bounds for the Stieltjes transform and the density of states of Wigner matrices ⋮ Sparse recovery from extreme eigenvalues deviation inequalities ⋮ Universality for the largest eigenvalue of sample covariance matrices with general population

Cites Work

• Local semicircle law and complete delocalization for Wigner random matrices
• A universality result for the smallest eigenvalues of certain sample covariance matrices
• Random matrices: The distribution of the smallest singular values
• Spectral analysis of large dimensional random matrices
• Semicircle law on short scales and delocalization of eigenvectors for Wigner random matrices
• Increasing subsequences and the hard-to-soft edge transition in matrix ensembles
• DISTRIBUTION OF EIGENVALUES FOR SOME SETS OF RANDOM MATRICES

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