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October 2018 Real eigenvalues in the non-Hermitian Anderson model
Ilya Goldsheid, Sasha Sodin
Ann. Appl. Probab. 28(5): 3075-3093 (October 2018). DOI: 10.1214/18-AAP1383

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.

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Ilya Goldsheid. Sasha Sodin. "Real eigenvalues in the non-Hermitian Anderson model." Ann. Appl. Probab. 28 (5) 3075 - 3093, October 2018. https://doi.org/10.1214/18-AAP1383

Information

Received: 1 December 2017; Published: October 2018
First available in Project Euclid: 28 August 2018

zbMATH: 06974773
MathSciNet: MR3847981
Digital Object Identifier: 10.1214/18-AAP1383

Subjects:
Primary: 47B36 , 47B80

Keywords: Anderson model , non-Hermitian , random Schrödinger , Sample

Rights: Copyright © 2018 Institute of Mathematical Statistics

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Vol.28 • No. 5 • October 2018
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