Spectral Radii of Products of Random Rectangular Matrices
Spectral Radii of Products of Random Rectangular Matrices
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DOI：
10.1007/s10959-019-00942-9
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发表时间：
2019-09
影响因子：
0.8
通讯作者：
Y. Qi;Mengzi Xie
中科院分区：
文献类型：
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作者：
Y. Qi;Mengzi Xie
我们构造了元素为独立同分布标准复高斯随机变量的独立随机矩形矩阵。设这两个矩形矩阵的乘积是n × n方阵。乘积矩阵特征值的最大绝对值称为谱半径。本文研究了当m随λ变化时乘积的极限谱半径甚至可以发散。给出了谱半径极限分布的完整描述。当矩形矩阵是正方形时，我们的结果简化为Jiang和Qi（J Theor Probab 30（1）：326-364，2017）中的结果。
We considermindependent random rectangular matrices whose entries are independent and identically distributed standard complex Gaussian random variables. Assume the product of themrectangular matrices is ann-by-nsquare matrix. The maximum absolute value of theneigenvalues of the product matrix is called spectral radius. In this paper, we study the limiting spectral radii of the product whenmchanges withnand can even diverge. We give a complete description for the limiting distribution of the spectral radius. Our results reduce to those in Jiang and Qi (J Theor Probab 30(1):326–364, 2017) when the rectangular matrices are square.