Products of Independent non-Hermitian Random Matrices

Sean O'Rourke (Rutgers University)
Alexander B. Soshnikov (University of California Davis)


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.

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Pages: 2219-2245

Publication Date: November 15, 2011

DOI: 10.1214/EJP.v16-954


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