On the spectrum of sum and product of non-hermitian random matrices

Details On the spectrum of sum and product of non-hermitian random matrices On the spectrum of sum and product of non-hermitian random matrices

2010-10-15

arxiv.org/abs/1010.3087v2

Electronic Communications in Probability 16 (2011), 104-113

Mathematics

Probability

8 pages, statement of main theorem slightly improved

Scientific paper

In this short note, we revisit the work of T. Tao and V. Vu on large non-hermitian random matrices with independent and identically distributed entries with mean zero and unit variance. We prove under weaker assumptions that the limit spectral distribution of sum and product of non-hermitian random matrices is universal. As a byproduct, we show that the generalized eigenvalues distribution of two independent matrices converges almost surely to the uniform measure on the Riemann sphere.

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