Limiting Empirical Spectral Distribution for Products of Rectangular Matrices

2021/04/07 by Yongcheng Qi, Qi, Yongcheng, Hongru Zhao +1
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.2104.03244

openalex publication_date 2021/04/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• On the distribution of the largest eigenvalue in principal components analysis

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