Real eigenvalues in the non-Hermitian Anderson model
Mathematical Physics
2021-09-28 v2 math.MP
Probability
Spectral Theory
Abstract
The eigenvalues of the Hatano--Nelson non-Hermitian Anderson matrices, in the spectral regions in which the Lyapunov exponent exceeds the non-Hermiticity parameter, are shown to be real and exponentially close to the Hermitian eigenvalues. This complements previous results, according to which the eigenvalues in the spectral regions in which the non-Hermiticity parameter exceeds the Lyapunov exponent are aligned on curves in the complex plane.
Keywords
Cite
@article{arxiv.1707.02181,
title = {Real eigenvalues in the non-Hermitian Anderson model},
author = {Ilya Goldsheid and Sasha Sodin},
journal= {arXiv preprint arXiv:1707.02181},
year = {2021}
}
Comments
21 pp., 2 fig; to appear in Ann. Appl. Probab