Limiting empirical spectral distribution for products of rectangular matrices

Yongcheng Qi, Hongru Zhao

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Article number125237
JournalJournal of Mathematical Analysis and Applications
Volume502
Issue number2
DOIs
StatePublished - Oct 15 2021

Bibliographical note

Funding Information:
The authors would like to thank an anonymous referee for his/her careful reading of the manuscript and suggestion which has improved the layout of the manuscript. The research of Yongcheng Qi was supported in part by NSF Grant DMS-1916014 .

Publisher Copyright:
© 2021 Elsevier Inc.

Keywords

  • Eigenvalues
  • Empirical spectral distribution
  • Non-Hermitian random matrix
  • Product of rectangular matrices

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