重叠随机Wishart矩阵谱的三维高斯起伏

IF 0.9 4区数学 Q4 PHYSICS, MATHEMATICAL Random Matrices-Theory and Applications Pub Date : 2021-12-27 DOI:10.1142/s2010326322500484

Jeffrey Kuan, Zhengye Zhou

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引用次数: 1

摘要

在[DP18]中，作者考虑重叠的Wishart矩阵的特征值，并证明其涨落渐近收敛于高斯自由场。在这篇简短的笔记中，推广了他们的结果，表明当矩阵项进行随机演化时，涨落渐近收敛到三维高斯场，该场具有显式的轮廓积分公式。这与随机维格纳矩阵[Bor14]的结果类似。

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Three-dimensional Gaussian fluctuations of spectra of overlapping stochastic Wishart matrices

In [DP18], the authors consider eigenvalues of overlapping Wishart matrices and prove that its fluctuations asymptotically convergence to the Gaussian free field. In this brief note, their result is extended to show that when the matrix entries undergo stochastic evolution, the fluctuations asymptotically converge to a three-dimensional Gaussian field, which has an explicit contour integral formula. This is analogous to the result of [Bor14] for stochastic Wigner matrices.

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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.