Аннотация:
For fixed m>1, we consider m independent n×n non-Hermitian random matrices X1,…,Xm with i.i.d. centered entries with a finite (2+η)-th moment, η>0. As n tends to infinity, we show that the empirical spectral distribution of X=n−m/2∗X1X2⋯Xm converges, with probability 1, to a non-random, rotationally invariant distribution with compact support in the complex plane. The limiting distribution is the m-th power of the circular law. This is a joint work with Sean O'Rourke. The preprint is available at http://arxiv.org/abs/1012.4497.