单位矩阵的秩一乘法扰动动力学

IF 0.9 4区数学 Q4 PHYSICS, MATHEMATICAL Random Matrices-Theory and Applications Pub Date : 2024-05-21 DOI:10.1142/s2010326324500072

Guillaume Dubach, Jana Reker

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引用次数: 0

摘要

我们对费奥多罗夫提出的单位矩阵乘法扰动模型进行了动力学研究。特别是，我们确定了一个确定性域流，它以高概率约束频谱，在所有次临界时间尺度上将离群值与典型特征值分离开来。这些结果是在 U 的一般假设下获得的，这些假设对各种单元随机矩阵模型都成立。

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Dynamics of a rank-one multiplicative perturbation of a unitary matrix

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.

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来源期刊

Random Matrices-Theory and Applications Decision Sciences-Statistics, Probability and Uncertainty

CiteScore

1.90

自引率

11.10%

发文量

期刊介绍： Random Matrix Theory (RMT) has a long and rich history and has, especially in recent years, shown to have important applications in many diverse areas of mathematics, science, and engineering. The scope of RMT and its applications include the areas of classical analysis, probability theory, statistical analysis of big data, as well as connections to graph theory, number theory, representation theory, and many areas of mathematical physics. Applications of Random Matrix Theory continue to present themselves and new applications are welcome in this journal. Some examples are orthogonal polynomial theory, free probability, integrable systems, growth models, wireless communications, signal processing, numerical computing, complex networks, economics, statistical mechanics, and quantum theory. Special issues devoted to single topic of current interest will also be considered and published in this journal.