Products of independent Gaussian random matrices
Products of independent Gaussian random matrices
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发表时间：
2015-10
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通讯作者：
J. R. Ipsen
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作者：
J. R. Ipsen
本文从精确求解高斯随机矩阵模型的角度综述了随机矩阵积的研究进展。我们导出了任意矩阵维数下的特征值和奇异值的相关函数的精确公式。这些精确的结果用于研究当矩阵维数或因子数趋于无穷时宏观密度和微观相关性的渐近极限。
This thesis reviews recent progress on products of random matrices from the perspective of exactly solved Gaussian random matrix models. We derive exact formulae for the correlation functions for the eigen- and singular values at arbitrary matrix dimension and for an arbitrary number of factors. These exact results are used to study asymptotic limits for the macroscopic densities and the microscopic correlations as either the matrix dimension or the number of factors tends to infinity.