Real eigenvalues in the non-hermitian anderson model

Ilya Goldsheid, Sasha Sodin

Research output: Contribution to journalArticlepeer-review

2 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 languageEnglish
Pages (from-to)3075-3093
Number of pages19
JournalAnnals of Applied Probability
Volume28
Issue number5
DOIs
StatePublished - Oct 2018

Funding

FundersFunder number
Horizon 2020 Framework Programme639305
Royal Society
European Research Council

    Keywords

    • Anderson model
    • Non-hermitian
    • Random schrödinger
    • Sample

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