On the one hand, we prove that almost surely, for large dimension, there is eigenvalue of a Hermitian polynomial in independent Wigner and deterministic, in any interval lying at some distance from the supports of a of deterministic probability measures, which is computed with the of free probability. On the other hand, we establish the strong freeness of independent Wigner matrices and any family of matrices with strong limiting distribution.
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Belinschi et al. (2016) studied this question.
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