Limiting Empirical Spectral Distribution for Products of Rectangular Matrices

Abstract

In this paper, we consider $m$ independent random rectangular matrices whose entries are independent and identically distributed standard complex Gaussian random variables and assume the product of the $m$ rectangular matrices is an $n$ by $n$ square matrix. We study the limiting empirical spectral distributions of the product where the dimension of the product matrix goes to infinity, and $m$ may change with the dimension of the product matrix and diverge. We give a complete description for the limiting distribution of the empirical spectral distributions for the product matrix and illustrate some examples.

References in corpus (2)

• On the Asymptotic Spectrum of Products of Independent Random Matrices
• Products of independent elliptic random matrices

Cited by in corpus (1)

• On eigenvalue distributions of large auto-covariance matrices