We provide a dynamical study of a model of multiplicative perturbation of a unitary matrix introduced by Fyodorov. In particular, we identify a flow of deterministic domains that bound the spectrum with high probability, separating the outlier from the typical eigenvalues at all sub-critical timescales. These results are obtained under generic assumptions on $U$ that hold for a variety of unitary random matrix models.

中文翻译：

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酉矩阵的一阶乘性摄动的动力学

我们对 Fyodorov 引入的酉矩阵乘法微扰模型进行了动力学研究。特别是，我们确定了以高概率限制频谱的确定性域流，将所有亚临界时间尺度的异常值与典型特征值分开。这些结果是在 $U$ 的通用假设下获得的，该假设适用于各种酉随机矩阵模型。