The spectra of random abelian G-circulant matrices
Probability
2012-08-17 v2
Abstract
This paper studies the asymptotic behavior of eigenvalues of random abelian G-circulant matrices, that is, matrices whose structure is related to a finite abelian group G in a way that naturally generalizes the relationship between circulant matrices and cyclic groups. It is shown that, under mild conditions, when the size of the group G goes to infinity, the spectral measures of such random matrices approach a deterministic limit. Depending on some aspects of the structure of the groups, whether the matrices are constrained to be Hermitian, and a few details of the distributions of the matrix entries, the limit measure is either a (complex or real) Gaussian distribution or a mixture of two Gaussian distributions.
Keywords
Cite
@article{arxiv.1109.5675,
title = {The spectra of random abelian G-circulant matrices},
author = {Mark W. Meckes},
journal= {arXiv preprint arXiv:1109.5675},
year = {2012}
}