Limiting eigenvalue distributions of block random matrices with one-dimensional coupling structure

Toshiyuki Tanaka

Abstract: We study limiting eigenvalue distributions of block random matrix ensembles with one-dimensional coupling structure under the limit where the matrix size tends to infinity. Matrices in the ensembles have independent real symmetric random matrices of Wigner type on the diagonal blocks and a scalar multiple of the identity matrix on the blocks adjacent to the diagonal blocks. Explicit analytical formulas for the limiting eigenvalue distributions are derived for the 2 × 2-block ensemble as well as the 3 × 3-block circular ensemble. Further numerical results for B × B-block ensembles with B ≥ 3 are also shown.