Limit Theorems for Spectra of Circulant Block Matrices with Large Random Blocks

Abstract

This paper investigates the spectral properties of block circulant matrices with high-order symmetric (or Hermitian) blocks. We analyze cases with dependent or sparse independent entries within these blocks. Additionally, we analyze the distribution of singular values for the product of independent circulant matrices with non-Hermitian blocks.

Keywords

• random matrices
• circulant matrices
• semicircle law