Products of independent elliptic random matrices
  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. 
Sean O'Rourke, David Renfrew, Alexander Soshnikov, and Van Vu
math.PR math-ph math.MP