Statistical properties of eigenvalues of an ensemble of pseudo-Hermitian Gaussian matrices
Statistical Mechanics
2020-08-28 v1 Mathematical Physics
math.MP
Abstract
We investigate the statistical properties of eigenvalues of pseudo-Hermitian random matrices whose eigenvalues are real or complex conjugate. It is shown that when the spectrum splits into separated sets of real and complex conjugate eigenvalues, the real ones show characteristics of an intermediate incomplete spectrum, that is, of a so-called thinned ensemble. On the other hand, the complex ones show repulsion compatible with cubic-order repulsion of non normal matrices for the real matrices, but higher order repulsion for the complex and quaternion matrices.
Keywords
Cite
@article{arxiv.2008.12088,
title = {Statistical properties of eigenvalues of an ensemble of pseudo-Hermitian Gaussian matrices},
author = {Gabriel Marinello and Mauricio Porto Pato},
journal= {arXiv preprint arXiv:2008.12088},
year = {2020}
}