We study the fluctuations associated to the a.s. convergence of the outliers established by Belinschi–Bercovici–Capitaine of an Hermitian polynomial in a complex Wigner matrix and a spiked deterministic real diagonal matrix. Thus, we extend the nonuniversality phenomenon established by Capitaine–Donati-Martin–Féral for additive deformations of complex Wigner matrices, to any Hermitian polynomial. The result is described using the operator-valued subordination functions of free probability theory.

中文翻译：

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复 Wigner 矩阵和尖峰对角矩阵中 Hermitian 多项式异常值波动的非普遍性

我们研究了与复杂 Wigner 矩阵和尖峰确定性实对角矩阵中 Hermitian 多项式的 Belinschi-Bercovici-Capitaine 建立的异常值的收敛相关的波动。因此，我们将 Capitaine-Donati-Martin-Féral 建立的用于复杂 Wigner 矩阵的加性变形的非普遍性现象扩展到任何 Hermitian 多项式。使用自由概率论的算子值从属函数来描述结果。