On some spectral properties of large self-dual dilute quaternion random matrices

Abstract

In this paper, we study the spectral properties of the large self-dual dilute quaternion random matrices. For the dilute case, we prove that the empirical spectral distribution still converges to the semicircular law with some appropriate normalization. Further, we obtain the limits of the extreme eigenvalues of the large self-dual dilute quaternion random matrices under some moment assumptions of the underlying distributions and give a necessary condition for the strong convergence of the extreme eigenvalues.