正均值高斯矩阵的最大特征值

Arijit Chakrabarty, Rajat Subhra Hazra, Moumanti Podder
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引用次数: 0

摘要

这篇短文研究了具有正均值相关高斯条目的对称随机矩阵的最大特征值的波动。在假设协方差核是绝对可求和的情况下,证明了最大特征值在居中后,收敛于具有明确定义的均值和方差的正态分布。这一结果概括了对具有独立条目的维格纳矩阵的已知发现。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Largest eigenvalue of positive mean Gaussian matrices
This short note studies the fluctuations of the largest eigenvalue of symmetric random matrices with correlated Gaussian entries having positive mean. Under the assumption that the covariance kernel is absolutely summable, it is proved that the largest eigenvalue, after centering, converges in distribution to normal with an explicitly defined mean and variance. This result generalizes known findings for Wigner matrices with independent entries.
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