On Fluctuations of Matrix Entries of Regular Functions of Wigner Matrices with Non-Identically Distributed Entries
arXiv:1104.1663
Abstract
In this note, we extend the results about the fluctuations of the matrix entries of regular functions of Wigner random matrices obtained in arXiv:1103.3731 [math.PR] to Wigner matrices with non-i.i.d. entries provided certain Lindeberg type conditions for the fourth moments of the off-diagonal entries and the second moments of the diagonal entries are satisfied. In addition, we relax our conditions on the test functions and require that for some $s>3 \ \int (1+|k|)^{2s}\*|\hat{f}(k)|^2 \* dk <\infty.$
accepted for publication in Journal of Theoretical Probability
References in corpus (6)
- Central limit theorem for linear eigenvalue statistics of random matrices with independent entries
- Central Limit Theorem for linear eigenvalue statistics of the Wigner and sample covariance random matrices
- Rigidity of Eigenvalues of Generalized Wigner Matrices
- Non-Gaussian Limiting Laws for the Entries of Regular Functions of the Wigner Matrices
- On Finite Rank Deformations of Wigner Matrices
- Fluctuations of the extreme eigenvalues of finite rank deformations of random matrices