We consider m independent random rectangular matrices whose entries are independent and identically distributed standard complex Gaussian random variables. Assume the product of the m rectangular matrices is an n by n square matrix. The maximum absolute values of the n eigenvalues of the product matrix is called spectral radius. In this paper, we study the limiting spectral radii of the product when m changes with n and 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 [26] when the rectangular matrices are square ones.

中文翻译：

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随机矩形矩阵乘积的谱半径

我们考虑 m 个独立的随机矩形矩阵，其条目是独立同分布的标准复高斯随机变量。假设 m 个矩形矩阵的乘积是一个 n × n 方阵。乘积矩阵的 n 个特征值的最大绝对值称为谱半径。在本文中，我们研究了当 m 随 n 变化甚至可能发散时产品的极限谱半径。我们给出了谱半径的极限分布的完整描述。当矩形矩阵是方形矩阵时，我们的结果减少到 Jiang 和 Qi [26] 中的结果。