The Annals of Applied Probability

Real eigenvalues in the non-Hermitian Anderson model

Ilya Goldsheid and Sasha Sodin

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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.

Article information

Source
Ann. Appl. Probab., Volume 28, Number 5 (2018), 3075-3093.

Dates
Received: December 2017
First available in Project Euclid: 28 August 2018

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1535443242

Digital Object Identifier
doi:10.1214/18-AAP1383

Mathematical Reviews number (MathSciNet)
MR3847981

Zentralblatt MATH identifier
06974773

Subjects
Primary: 47B80: Random operators [See also 47H40, 60H25] 47B36: Jacobi (tridiagonal) operators (matrices) and generalizations

Keywords
Sample non-Hermitian Anderson model random Schrödinger

Citation

Goldsheid, Ilya; Sodin, Sasha. Real eigenvalues in the non-Hermitian Anderson model. Ann. Appl. Probab. 28 (2018), no. 5, 3075--3093. doi:10.1214/18-AAP1383. https://projecteuclid.org/euclid.aoap/1535443242


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