On the semicircular law of large dimensional random quaternion matrices

Abstract

It is well known that Gaussian symplectic ensemble (GSE) is defined on the space of $n\times n$ quaternion self-dual Hermitian matrices with Gaussian random elements. There is a huge body of literature regarding this kind of matrices. As a natural idea we want to get more universal results by removing the Gaussian condition. For the first step, in this paper we prove that the empirical spectral distribution of the common quaternion self-dual Hermitian matrices tends to semicircular law. The main tool to establish the universal result is given as a lemma in this paper as well.

20 pages

References in corpus (1)

• Semicircle Law for a Class of Random Matrices with Dependent Entries

Cited by in corpus (4)

• Convergence rates of the spectral distributions of large random quaternion self-dual Hermitian matrices
• On the limit of extreme eigenvalues of large dimensional random quaternion matrices
• Convergence of Empirical Spectral Distributions of Large Dimensional Quaternion Sample Covariance Matrices
• Convergence Rates of Spectral Distribution of Large Dimensional Quaternion Sample Covariance Matrix