Spectral analysis of large block random matrices with rectangular blocks

In this paper, we study the spectral properties of the large block random matrices when the blocks are general rectangular matrices. Under some moment assumptions of the underlying distributions, we prove the existence of the limiting spectral distribution (LSD) of the block random matrices. Further, we determine the Stieltjes transform of the LSD under the same moment conditions by demonstrating that it is the same as in the case where the underlying distributions are Gaussian.