Limiting spectral distribution for a class of random matrices

  title={Limiting spectral distribution for a class of random matrices},
  author={Y. Q. Yin},
  journal={Journal of Multivariate Analysis},
  • Y. Yin
  • Published 1 October 1986
  • Mathematics
  • Journal of Multivariate Analysis
Weak Convergence of random functions defined by the eigenvectors of sample covariance matrices
Let {v ij }, i, j = 1, 2,..., be i.i.d. symmetric random variables with E(v 4 11 ) 0 as n → ∞. Denote by O n Λ n O T n the spectral decomposition of M n . Define X ∈ D[0,1] by X n (t) = √n/2Σ [nt]
Weak Convergence of a Collection of Random Functions Defined by the Eigenvectors of Large Dimensional Random Matrices
For each n, let Un be Haar distributed on the group of n × n unitary matrices. Let xn,1, . . . ,xn,m denote orthogonal nonrandom unit vectors in C n and let un,k = (uk, . . . , u n k) ∗ = U∗ nxn,k, k
Strong convergence of the empirical distribution of eigenvalues of large dimensional random matrices
Let X be n - N containing i.i.d. complex entries with E X11 - EX112 = 1, and T an n - n random Hermitian nonnegative definite, independent of X. Assume, almost surely, as n --> [infinity], the
Circular Law Theorem for Random Markov Matrices
Let (Xi,j) be an infinite array of i.i.d. non negative real random variables with unit mean, finite positive variance σ, and finite fourth moment. Let M be the n×n random Markov matrix with i.i.d.
Spectral properties of sample covariance matrices arising from random matrices with independent non identically distributed columns
Given a random matrix X = (x1, . . . , xn) ∈ Mp,n with independent columns and satisfying concentration of measure hypotheses and a parameter z whose distance to the spectrum of 1 n XXT should not
Spectral convergence for a general class of random matrices
Let Bn = (1/N)T 1/2 n XnX∗ nT 1/2 n where Xn = (Xij ) is n × N with i.i.d. complex standardized entries having finite fourth moment, and T 1/2 n is a Hermitian square root of the nonnegative definite


Limit Theorem for the Eigenvalues of the Sample Covariance Matrix when the Underlying Distribution is Isotropic
In this paper, the authors show that the spectral distribution of the sample covariance matrix has a limit when the underlying distribution is isotropic, and the dimension p of this distribution and
The Strong Limits of Random Matrix Spectra for Sample Matrices of Independent Elements
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
Probability Inequalities for sums of Bounded Random Variables
Abstract Upper bounds are derived for the probability that the sum S of n independent random variables exceeds its mean ES by a positive number nt. It is assumed that the range of each summand of S
Spectral Analysis of Networks with Random Topologies
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
Maximum Properties and Inequalities for the Eigenvalues of Completely Continuous Operators.
  • K. Fan
  • Mathematics
    Proceedings of the National Academy of Sciences of the United States of America
  • 1951