We consider the product of a finite number of non-Hermitian random matrices with i.i.d. centered entries of growing size. We assume that the entries have a finite moment of order bigger than two. We show that the empirical spectral distribution of the properly normalized product converges, almost surely, to a non-random, rotationally invariant distribution with compact support in the complex plane. The limiting distribution is a power of the circular law.
"Products of Independent non-Hermitian Random Matrices." Electron. J. Probab. 16 2219 - 2245, 2011. https://doi.org/10.1214/EJP.v16-954