Convergence of Empirical Spectral Distributions of Large Dimensional Quaternion Sample Covariance Matrices

Abstract

In this paper we establish the limit of the empirical spectral distribution of quaternion sample covariance matrices. Suppose ${\mathbf{X}}_n=(x_{jk}^{(n)}{)}_{p\times n}$ is a quaternion random matrix. For each $n$, the entries $\{x_{ij}^{(n)}\}$ are independent random quaternion variables with a common mean $\mu$ and variance ${\sigma }^2>0$. It is shown that the empirical spectral distribution of the quaternion sample covariance matrix ${\mathbf{S}}_n=n^{-1}{\mathbf{X}}_n{\mathbf{X}}_n^{\ast }$ converges to the M-P law as $p\to \infty$, $n\to \infty$ and $p/n\to y\in (0,+\infty )$.

20 pages

References in corpus (1)

• On the semicircular law of large dimensional random quaternion matrices

Cited by in corpus (2)

• Extreme Eigenvalues of Large Dimensional Quaternion Sample Covariance Matrix
• Convergence Rates of Spectral Distribution of Large Dimensional Quaternion Sample Covariance Matrix