Central Limit Theorem for linear eigenvalue statistics of the Wigner and sample covariance random matrices
arXiv:1101.3249
Abstract
We consider two classical ensembles of the random matrix theory: the Wigner matrices and sample covariance matrices, and prove Central Limit Theorem for linear eigenvalue statistics under rather weak (comparing with results known before) conditions on the number of derivatives of the test functions and also on the number of the entries moments. Moreover, we develop a universal method which allows one to obtain automatically the bounds for the variance of differentiable test functions, if there is a bound for the variance of the trace of the resolvent of random matrix. The method is applicable not only to the Wigner and sample covariance matrices, but to any ensemble of random matrices.
18 pages
References in corpus (1)
Cited by in corpus (12)
- Mesoscopic linear statistics of Wigner matrices
- On the Spectral Form Factor for Random Matrices
- A Data Driven Approach for Resting-state EEG signal Classification of Schizophrenia with Control Participants using Random Matrix Theory
- Quantitative CLT for linear eigenvalue statistics of Wigner matrices
- Fluctuation of eigenvalues of symmetric circulant matrices with independent entries
- Central limit theorem for linear eigenvalue statistics of elliptic random matrices
- Improvement of Resting-state EEG Analysis Process with Spectrum Weight-Voting based on LES
- Central limit theorem for linear spectral statistics of general separable sample covariance matrices with applications
- Fluctuations of the Stieltjes transform of the empirical spectral distribution of selfadjoint polynomials in Wigner and deterministic diagonal matrices
- Multi-Point Functional Central Limit Theorem for Wigner Matrices
- Linear spectral statistics of sequential sample covariance matrices
- Test of Independence for High-dimensional Random Vectors Based on Block Correlation Matrices