  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.

Probability