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2011 On the spectrum of sum and product of non-hermitian random matrices
Charles Bordenave
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Electron. Commun. Probab. 16: 104-113 (2011). DOI: 10.1214/ECP.v16-1606

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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Charles Bordenave. "On the spectrum of sum and product of non-hermitian random matrices." Electron. Commun. Probab. 16 104 - 113, 2011. https://doi.org/10.1214/ECP.v16-1606

Information

Accepted: 12 February 2011; Published: 2011
First available in Project Euclid: 7 June 2016

zbMATH: 1227.60010
MathSciNet: MR2772389
Digital Object Identifier: 10.1214/ECP.v16-1606

Subjects:
Primary: 60B20
Secondary: 15A18‎, 47A10

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