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

Charles Bordenave (CNRS and University of Toulouse)

Abstract


In this note, we revisit the work of T. Tao and V. Vu on large non-hermitian random matrices with independent and identically distributed (i.i.d.) 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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Pages: 104-113

Publication Date: February 12, 2011

DOI: 10.1214/ECP.v16-1606

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