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Products of Independent Non-Hermitian Random Matrices

Mathematical Physics & Probability

Speaker: Sean O'Rourke, UC Davis
Location: 1147 MSB
Start time: Wed, Feb 2 2011, 4:10PM

For fixed m>1, we consider the product of m independent square non-Hermitian random matrices each of size n. As n tends to infinity, we show that the empirical spectral distribution of the product 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 joint work with Alexander Soshnikov.