大维一般信息加噪声型矩阵的极限谱分布分析

IF 0.8 4区数学 Q3 STATISTICS & PROBABILITY

Journal of Theoretical Probability Pub Date : 2023-07-28 DOI:10.1007/s10959-023-01276-3

Huanchao Zhou, Jiang Hu, Zhidong Bai, Jack W. Silverstein

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引用次数: 0

摘要

本文推导了Zhou (JTP 36:1203 - 1226,2023)研究的“一般信息加噪声”型非中心协方差矩阵的极限谱分布的解析行为。通过定义其Stieltjes变换的方程，证明了极限分布有一个远离零的连续导数，导数为正的地方是解析的，并给出了其支持度的判定准则。我们还扩展了Zhou (JTP 36:20 3- 1226,2023)的结果，以允许底层随机矩阵的行与列的所有可能的比率。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Analysis of the Limiting Spectral Distribution of Large-dimensional General Information-Plus-Noise-Type Matrices

In this paper, we derive the analytical behavior of the limiting spectral distribution of non-central covariance matrices of the “general information-plus-noise" type, as studied in Zhou (JTP 36:1203–1226, 2023). Through the equation defining its Stieltjes transform, it is shown that the limiting distribution has a continuous derivative away from zero, the derivative being analytic wherever it is positive, and we show the determination criterion for its support. We also extend the result in Zhou (JTP 36:1203-1226, 2023) to allow for all possible ratios of row to column of the underlying random matrix.

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来源期刊

Journal of Theoretical Probability 数学-统计学与概率论

CiteScore

1.50

自引率

12.50%

发文量

审稿时长

6-12 weeks

期刊介绍： Journal of Theoretical Probability publishes high-quality, original papers in all areas of probability theory, including probability on semigroups, groups, vector spaces, other abstract structures, and random matrices. This multidisciplinary quarterly provides mathematicians and researchers in physics, engineering, statistics, financial mathematics, and computer science with a peer-reviewed forum for the exchange of vital ideas in the field of theoretical probability.