The Spherical Law for products of random matrices

Let $\{A_N\}$ and $\{B_N\}$ be sequences of matrices whose entries are independent complex random variables with zero mean and unit variance. Then the spectral densities of the matrices $A_NB_N^{-1}$ converge to the uniform density on the Riemann sphere.

The Spherical Law. The spectral densities of $A_NB_N^{-1}$ converge to the uniform density on the Riemann sphere as $N$ tends to infinity.

This is proposed as an analogue of the circular law for products involving the inverse of a random matrix. The supplied text does not establish the claim or provide evidence resolving its validity.