Mathematics Colloquia and Seminars

Return to Colloquia & Seminar listing

Description

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.