## Tables from this paper

## 370 Citations

### Limit theorems for linear eigenvalue statistics of overlapping matrices

- Mathematics, Computer Science
- 2014

Several limit theorems for linear eigenvalue statistics of overlapping Wigner and sample covariance matrices are proved, based on a graph-theoretic interpretation of the Chebyshev linear statistics as sums over non-backtracking cyclic paths.

### On Asymptotic Behavior of Multilinear Eigenvalue Statistics of Random Matrices

- Mathematics
- 2008

We prove the Law of Large Numbers and the Central Limit Theorem for analogs of U- and V- (von Mises) statistics of eigenvalues of random matrices as their size tends to infinity. We show first that…

### Universality results for the largest eigenvalues of some sample covariance matrix ensembles

- Mathematics, Computer Science
- 2007

This paper extends the well-known result of Soshnikov that the limiting distribution of the largest eigenvalue is same that of Gaussian samples to two cases, when the ratio approaches an arbitrary finite value and the ratio becomes infinite or arbitrarily small.

### Fluctuations for linear eigenvalue statistics of sample covariance matrices

- Mathematics
- 2018

We prove a central limit theorem for the difference of linear eigenvalue statistics of a sample covariance matrix W̃ and its minor W . We find that the fluctuation of this difference is much smaller…

### Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices

- MathematicsRandom Matrices: Theory and Applications
- 2019

We prove a central limit theorem for the difference of linear eigenvalue statistics of a sample covariance matrix [Formula: see text] and its minor [Formula: see text]. We find that the fluctuation…

### Fluctuations for linear eigenvalue statistics of sample covariance random matrices

- Mathematics
- 2018

We prove a central limit theorem for the difference of linear eigenvalue statistics of a sample covariance matrix $\widetilde{W}$ and its minor $W$. We find that the fluctuation of this difference is…

### PROPERTIES OF EIGENVALUES AND EIGENVECTORS OF LARGE DIMENSIONAL SAMPLE CORRELATION MATRICES

- Mathematics
- 2021

This paper is to study the properties of eigenvalues and eigenvectors of high dimensional sample correlation matrices. We firstly improve the result of Jiang (2004); Xiao and Zhou (2010) and the…

### On the limit of the largest eigenvalue of the large dimensional sample covariance matrix

- Mathematics
- 1988

SummaryIn this paper the authors show that the largest eigenvalue of the sample covariance matrix tends to a limit under certain conditions when both the number of variables and the sample size tend…

### On the empirical distribution of eigenvalues of a class of large dimensional random matrices

- Mathematics
- 1995

A stronger result on the limiting distribution of the eigenvalues of random Hermitian matrices of the form A + XTX*, originally studied in Marcenko and Pastur, is presented. Here, X(N - n), T(n - n),…

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