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Real eigenvalues in the non-Hermitian Anderson model. (English) Zbl 06974773

Summary: 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.

MSC:

47B80 Random linear operators
47B36 Jacobi (tridiagonal) operators (matrices) and generalizations
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