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2021 Outlier eigenvalues for non-Hermitian polynomials in independent i.i.d. matrices and deterministic matrices
Serban Belinschi, Charles Bordenave, Mireille Capitaine, Guillaume Cébron
Author Affiliations +
Electron. J. Probab. 26: 1-37 (2021). DOI: 10.1214/21-EJP666

Abstract

We consider a square random matrix of size N of the form P(Y,A) where P is a noncommutative polynomial, A is a tuple of deterministic matrices converging in ∗-distribution, when N goes to infinity, towards a tuple a in some C-probability space and Y is a tuple of independent matrices with i.i.d. centered entries with variance 1N. We investigate the eigenvalues of P(Y,A) outside the spectrum of P(c,a) where c is a circular system which is free from a. We provide a sufficient condition to guarantee that these eigenvalues coincide asymptotically with those of P(0,A).

Funding Statement

G. C. was partly supported by the Project MESA (ANR-18-CE40-006) of the French National Research Agency (ANR).

Acknowledgments

The authors want to thank an anonymous referee for his very careful reading and his pertinent comments.

Citation

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Serban Belinschi. Charles Bordenave. Mireille Capitaine. Guillaume Cébron. "Outlier eigenvalues for non-Hermitian polynomials in independent i.i.d. matrices and deterministic matrices." Electron. J. Probab. 26 1 - 37, 2021. https://doi.org/10.1214/21-EJP666

Information

Received: 25 June 2020; Accepted: 13 June 2021; Published: 2021
First available in Project Euclid: 7 July 2021

Digital Object Identifier: 10.1214/21-EJP666

Subjects:
Primary: 15B52, 46L54, 60B20
Secondary: 15A18‎, 60F05

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