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

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 $O(n^{-1\mathrm{/}2})$ and the spectral distribution itself converges to the semicircular law in rates $O_p(n^{-2\mathrm{/}5})$ and $O_{a\mathrm{.}s\mathrm{.}}(n^{-2\mathrm{/}5+\eta })$. Those results include GSE as a special case.