Spectral properties of polynomials in independent Wigner and deterministic matrices

Serban Belinschi; Mireille Capitaine

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arXiv · 1611.07440

Spectral properties of polynomials in independent Wigner and deterministic matrices

Serban Belinschi·Mireille Capitaine

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Abstract

On the one hand, we prove that almost surely, for large dimension, there is no eigenvalue of a Hermitian polynomial in independent Wigner and deterministic matrices, in any interval lying at some distance from the supports of a sequence of deterministic probability measures, which is computed with the tools of free probability. On the other hand, we establish the strong asymptotic freeness of independent Wigner matrices and any family of deterministic matrices with strong limiting distribution.

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Serban Belinschi, Mireille Capitaine. 2016-11-22. Spectral properties of polynomials in independent Wigner and deterministic matrices. https://arxiv.org/abs/1611.07440

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