Tables from this paper
368 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),…
References
SHOWING 1-10 OF 15 REFERENCES
The Strong Limits of Random Matrix Spectra for Sample Matrices of Independent Elements
- Mathematics
- 1978
This paper proves almost-sure convergence of the empirical measure of the normalized singular values of increasing rectangular submatrices of an infinite random matrix of independent elements. The…
Asymptotic distribution of eigenvalues of random matrices
- Mathematics, Physics
- 1972
The impetus for this paper comes mainly from work done in recent years by a number of physicists on a statistical theory of spectra. The book by M. L. Mehta [10] and the collection of reprints edited…
Characteristic Vectors of Bordered Matrices with Infinite Dimensions I
- Physics
- 1955
The statistical properties of the characteristic values of a matrix the elements of which show a normal (Gaussian) distribution are well known (cf. [6] Chapter XI) and have been derived, rather…
Statistical theory of energy levels and random matrices in physics
- Mathematics
- 1973
In this paper the physical aspects of the statistical theory of the energy levels of complex physical systems and their relation to the mathematical theory of random matrices are discussed. After a…
Linear Statistical Inference and its Applications.
- Mathematics
- 1966
Algebra of Vectors and Matrices. Probability Theory, Tools and Techniques. Continuous Probability Models. The Theory of Least Squares and Analysis of Variance. Criteria and Methods of Estimation.…
Spectral Analysis of Networks with Random Topologies
- Mathematics
- 1977
A class of neural models is introduced in which the topology of the neural network has been generated by a controlled probability model. It is shown that the resulting linear operator has a spectral…
On the Distribution of the Roots of Certain Symmetric Matrices
- Mathematics, Computer Science
- 1958
The distribution law obtained before' for a very special set of matrices is valid for much more general sets of real symmetric matrices of very high dimensionality.
An Introduction to Multivariate Statistical Analysis
- Mathematics
- 1959
Preface to the Third Edition.Preface to the Second Edition.Preface to the First Edition.1. Introduction.2. The Multivariate Normal Distribution.3. Estimation of the Mean Vector and the Covariance…