Real eigenvalues in the non-hermitian anderson model

Ilya Goldsheid; Sasha Sodin

doi:10.1214/18-AAP1383

Real eigenvalues in the non-hermitian anderson model

Ilya Goldsheid, Sasha Sodin

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

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.

Original language	English
Pages (from-to)	3075-3093
Number of pages	19
Journal	Annals of Applied Probability
Volume	28
Issue number	5
DOIs	https://doi.org/10.1214/18-AAP1383
State	Published - Oct 2018
Externally published	Yes

Bibliographical note

Publisher Copyright:
© Institute of Mathematical Statistics, 2018.

Keywords

Anderson model
Non-hermitian
Random schrödinger
Sample

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KW - Anderson model

KW - Non-hermitian

KW - Random schrödinger

KW - Sample

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ER -

Real eigenvalues in the non-hermitian anderson model

Abstract

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Keywords

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