Abstract
We consider a square random matrix of size N of the form 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 -probability space and Y is a tuple of independent matrices with i.i.d. centered entries with variance . We investigate the eigenvalues of outside the spectrum of 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 .
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
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
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