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

Alexander Tikhomirov (), Sabina Gulyaeva and Dmitry Timushev
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Alexander Tikhomirov: Institute of Physics and Mathematics, Komi SC UB RAS, Syktyvkar 167982, Russia
Sabina Gulyaeva: Institute of Exact Sciences and IT, Pitirim Sorokin Syktyvkar State University, Syktyvkar 167001, Russia
Dmitry Timushev: Institute of Physics and Mathematics, Komi SC UB RAS, Syktyvkar 167982, Russia

Mathematics, 2024, vol. 12, issue 14, 1-16

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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