Convergence rates of the spectral distributions of large random quaternion self-dual Hermitian matrices

Abstract

In this paper, convergence rates of the spectral distributions of quaternion self-dual Hermitian matrices are investigated. We show that under conditions of finite 6th moments, the expected spectral distribution of a large quaternion self-dual Hermitian matrix converges to the semicircular law in a rate of $O(n^{-1/2})$ and the spectral distribution itself converges to the semicircular law in rates $O_p(n^{-2/5})$ and $O_{a.s.}(n^{-2/5+\eta })$. Those results include GSE as a special case.

References in corpus (6)

• Level-Spacing Distributions and the Airy Kernel
• Level-Spacing Distributions and the Airy Kernel
• Extreme Value Statistics of Eigenvalues of Gaussian Random Matrices
• The largest eigenvalue of real symmetric, Hermitian and Hermitian self-dual random matrix models with rank one external source, part I
• On the limit of extreme eigenvalues of large dimensional random quaternion matrices
• On the semicircular law of large dimensional random quaternion matrices

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