Pseudo-Hermitian $$\beta $$ β -Ensembles with Complex Eigenvalues

Abstract

Pseudo-Hermitian and PT-symmetric matrices have been a topic of interest since the first papers on the subject in the late 90s. In this paper we utilize properties of tridiagonal random matrices described in the framework of generalized β ensembles to explore variations of that ensemble, which cause the eigenvalues to move from the real line into the complex plane in conjugate pairs, while still maintaining the pseudo-Hermitian property.