Anisotropic local laws for random matrices
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Publication:682801
DOI10.1007/s00440-016-0730-4zbMath1382.15051arXiv1410.3516OpenAlexW1576778649MaRDI QIDQ682801
Publication date: 5 February 2018
Published in: Probability Theory and Related Fields (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1410.3516
eigenvaluesphase transitionsrandom matrixWigner matriceslocal lawsample covariance matricesTracy-Widom-Airy statistics
Random matrices (probabilistic aspects) (60B20) Eigenvalues, singular values, and eigenvectors (15A18) Random matrices (algebraic aspects) (15B52)
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Cites Work
- Fluctuations at the edges of the spectrum of the full rank deformed GUE
- Spectral statistics of Erdős-Rényi graphs. I: Local semicircle law
- Averaging fluctuations in resolvents of random band matrices
- The local semicircle law for a general class of random matrices
- Tracy-Widom distribution for the largest eigenvalue of real sample covariance matrices with general population
- Local law of addition of random matrices on optimal scale
- Random matrices: universality of local eigenvalue statistics
- Universality of random matrices and local relaxation flow
- Rigidity of eigenvalues of generalized Wigner matrices
- Local single ring theorem
- Spectral statistics of Erdős-Rényi graphs II: eigenvalue spacing and the extreme eigenvalues
- Large complex correlated Wishart matrices: fluctuations and asymptotic independence at the edges
- Local semicircle law and complete delocalization for Wigner random matrices
- Characteristic vectors of bordered matrices with infinite dimensions
- A generalization of the Lindeberg principle
- Central limit theorem for linear eigenvalue statistics of random matrices with independent entries
- Spectral analysis of large dimensional random matrices
- No eigenvalues outside the support of the limiting spectral distribution of large-dimensional sample covariance matrices
- Level-spacing distributions and the Airy kernel
- Exact separation of eigenvalues of large dimensional sample covariance matrices
- On the empirical distribution of eigenvalues of a class of large dimensional random matrices
- Analysis of the limiting spectral distribution of large dimensional random matrices
- On orthogonal and symplectic matrix ensembles
- Bulk universality for generalized Wigner matrices
- On bilinear forms based on the resolvent of large random matrices
- Universality for the largest eigenvalue of sample covariance matrices with general population
- Subordination for the sum of two random matrices
- From Gumbel to Tracy-Widom
- Tracy-Widom limit for the largest eigenvalue of a large class of complex sample covariance matrices
- The Tracy-Widom limit for the largest eigenvalues of singular complex Wishart matrices
- The local relaxation flow approach to universality of the local statistics for random matrices
- Isotropic local laws for sample covariance and generalized Wigner matrices
- Universality of covariance matrices
- On the principal components of sample covariance matrices
- The Isotropic Semicircle Law and Deformation of Wigner Matrices
- Edge universality for deformed Wigner matrices
- DISTRIBUTION OF EIGENVALUES FOR SOME SETS OF RANDOM MATRICES
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