Non-Hermitian β-ensemble with real eigenvalues

Abstract

By removing the Hermitian condition of the so-called β-ensemble of tridiagonal matrices, an ensemble of non-Hermitian random matrices is constructed whose eigenvalues are all real. It is shown that they belong to the class of pseudo-Hermitian operators. Its statistical properties are investigated. © 2013 Copyright 2013 Author(s). This article is distributed under a Creative Commons Attribution 3.0 Unported License.