The Annals of Applied Probability

Real eigenvalues in the non-Hermitian Anderson model

Ilya Goldsheid and Sasha Sodin

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Sample non-Hermitian Anderson model random Schrödinger


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.

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