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Pré-Publication, Document De Travail Année : 2020

Outlier eigenvalues for non-Hermitian polynomials in independent i.i.d. matrices and deterministic matrices

Mireille Capitaine
Guillaume Cébron Cébron

Résumé

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 1/N. 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).
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Dates et versions

hal-03023644 , version 1 (25-11-2020)

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Serban Belinschi, Charles Bordenave, Mireille Capitaine, Guillaume Cébron Cébron. Outlier eigenvalues for non-Hermitian polynomials in independent i.i.d. matrices and deterministic matrices. 2020. ⟨hal-03023644⟩
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