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Article Dans Une Revue Electronic Communications in Probability Année : 2011

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

Résumé

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.

Dates et versions

hal-00948941 , version 1 (18-02-2014)

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Charles Bordenave. On the spectrum of sum and product of non-Hermitian random matrices. Electronic Communications in Probability, 2011, 16, pp.104-113. ⟨10.1214/ECP.v16-1606⟩. ⟨hal-00948941⟩
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