块wigner型矩阵线性谱统计量的中心极限定理

IF 0.9 4区数学 Q4 PHYSICS, MATHEMATICAL

Random Matrices-Theory and Applications Pub Date : 2021-10-23 DOI:10.1142/s2010326323500065

Zheng-G Wang, Jianfeng Yao

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引用次数: 2

摘要

在随机块模型的激励下，研究了一类具有一定块结构的wigner型矩阵，利用局域律的大偏差界和累积展开公式建立了相应线性谱统计量的CLT。我们将结果应用于随机块模型。具体来说，一类重规格化邻接矩阵将是块wigner型矩阵。进一步，我们表明，对于这种重归一化邻接矩阵的某些估计量，它将不再是wigner型，而是在条目之间具有长期非衰减弱相关性，这种估计量的线性谱统计量仍然与块wigner型矩阵的线性谱统计量具有相同的极限行为，从而能够对随机块模型进行假设检验。

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Central Limit Theorem for Linear Spectral Statistics of Block-Wigner-type Matrices

Motivated by the stochastic block model, we investigate a class of Wigner-type matrices with certain block structures, and establish a CLT for the corresponding linear spectral statistics via the large-deviation bounds from local law and the cumulant expansion formula. We apply the results to the stochastic block model. Specifically, a class of renormalized adjacency matrices will be block-Wigner-type matrices. Further, we show that for certain estimator of such renormalized adjacency matrices, which will be no longer Wigner-type but share long-range non-decaying weak correlations among the entries, the linear spectral statistics of such estimators will still share the same limiting behavior as those of the block-Wigner-type matrices, thus enabling hypothesis testing about stochastic block model.

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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.