Convergence rates of the spectral distributions of large random quaternion self-dual Hermitian matrices (Q2254911)

The authors investigate convergence rates of the spectral distributions of quaternion self-dual Hermitian matrices. They 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 \(O_{a.s.} (n^{-2/5+\eta})\). These results include GSE as a special case.