Random matrices: Universality of local eigenvalue statistics
arXiv:0906.0510
Abstract
In this paper, we consider the universality of the local eigenvalue statistics of random matrices. Our main result shows that these statistics are determined by the first four moments of the distribution of the entries. As a consequence, we derive the universality of eigenvalue gap distribution and -point correlation and many other statistics (under some mild assumptions) for both Wigner Hermitian matrices and Wigner real symmetric matrices.
67 pages; to appear, Acta Math. Some additional corrections and references
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Cited by in corpus (19)
- Some Open Problems in Random Matrix Theory and the Theory of Integrable Systems. II
- Gaussian Fluctuations of Eigenvalues in Wigner Random Matrices
- Bulk universality for generalized Wigner matrices
- Rigidity of Eigenvalues of Generalized Wigner Matrices
- Stein's method in high dimensions with applications
- Universality of Random Matrices and Local Relaxation Flow
- The local relaxation flow approach to universality of the local statistics for random matrices
- Bulk Universality for Wigner Matrices
- Eigenvector Distribution of Wigner Matrices
- Universality for generalized Wigner matrices with Bernoulli distribution
- Random matrices: Universal properties of eigenvectors
- Universality of Wigner Random Matrices
- Universality of sine-kernel for Wigner matrices with a small Gaussian perturbation
- Limit Theorems for Beta-Jacobi Ensembles
- Average Density of States for Hermitian Wigner Matrices
- Zooming in on local level statistics by supersymmetric extension of free probability
- Spectral Properties of Wigner Matrices
- On Universality of Bulk Local Regime of the Deformed Laguerre Ensemble
- Asymptotic spectral independence of Wigner ensembles