某些加标矩阵的光谱测量偏差较大

IF 0.9 4区数学 Q4 PHYSICS, MATHEMATICAL Random Matrices-Theory and Applications Pub Date : 2020-09-26 DOI:10.1142/s2010326322500393

Nathan Noiry, A. Rouault

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引用次数: 1

摘要

我们证明了摄动(或尖刺)矩阵模型在摄动特征向量方向上的谱测量的大偏差原理。在研究的每个模型中，我们提供了两种方法，其中一种方法依赖于先前工作“通过大偏差求和规则”(Gamboa et al.[通过大偏差求和规则，J. Funct.])中导出的无扰动模型的大偏差原理。肛门。270(2)(2016)509-559]。

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Large deviations for spectral measures of some spiked matrices

We prove large deviations principles for spectral measures of perturbed (or spiked) matrix models in the direction of an eigenvector of the perturbation. In each model under study, we provide two approaches, one of which relying on large deviations principle of unperturbed models derived in the previous work “Sum rules via large deviations” (Gamboa et al. [Sum rules via large deviations, J. Funct. Anal. 270(2) (2016) 509–559]).

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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.