In this paper, we consider m independent random rectangular matrices whose entries are independent and identically distributed standard complex Gaussian random variables and assume the product of the m rectangular matrices is an n by n square matrix. We study the limiting empirical spectral distributions of the product where the dimension of the product matrix goes to infinity, and m may change with the dimension of the product matrix and diverge. We give a complete description for the limiting distribution of the empirical spectral distributions for the product matrix and illustrate some examples.

中文翻译：

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限制矩形矩阵乘积的经验光谱分布

在本文中，我们考虑m个独立的随机矩形矩阵，它们的条目是独立且均匀分布的标准复高斯随机变量，并假设m个矩形矩阵的乘积为n × n方阵。我们研究了产品的极限经验光谱分布，其中产品矩阵的维数变为无穷大，并且m可能随产品矩阵的维数而变化并发散。我们对乘积矩阵的经验光谱分布的极限分布给出了完整的描述，并举例说明了一些例子。