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2011 Products of Independent non-Hermitian Random Matrices
Sean O'Rourke, Alexander Soshnikov
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Electron. J. Probab. 16: 2219-2245 (2011). DOI: 10.1214/EJP.v16-954

Abstract

We consider the product of a finite number of non-Hermitian random matrices with i.i.d. centered entries of growing size. We assume that the entries have a finite moment of order bigger than two. We show that the empirical spectral distribution of the properly normalized product converges, almost surely, to a non-random, rotationally invariant distribution with compact support in the complex plane. The limiting distribution is a power of the circular law.

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Sean O'Rourke. Alexander Soshnikov. "Products of Independent non-Hermitian Random Matrices." Electron. J. Probab. 16 2219 - 2245, 2011. https://doi.org/10.1214/EJP.v16-954

Information

Accepted: 15 November 2011; Published: 2011
First available in Project Euclid: 1 June 2016

zbMATH: 1244.60011
MathSciNet: MR2861673
Digital Object Identifier: 10.1214/EJP.v16-954

Subjects:
Primary: 60B20

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