Limiting empirical spectral distribution for products of rectangular matrices

[摘要] 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. (c) 2021 Elsevier Inc. All rights reserved.

[发布日期] 2021-10-15

[关键词] Empirical spectral distribution;Eigenvalues;Product of rectangular matrices;Non-Hermitian random matrix