  For fixed $m > 1$, we study the product of $m$ independent $N \times N$
elliptic random matrices as $N$ tends to infinity. Our main result shows that
the empirical spectral distribution of the product converges, with probability
$1$, to the $m$-th power of the circular law, regardless of the joint
distribution of the mirror entries in each matrix. This leads to a new kind of
universality phenomenon: the limit law for the product of independent random
matrices is independent of the limit laws for the individual matrices
themselves.
  Our result also generalizes earlier results of G\"otze-Tikhomirov and
O'Rourke-Soshnikov concerning the product of independent iid random matrices.
