Spectral statistics of non-selfadjoint operators subject to small random perturbations. (English) Zbl 1475.35437
Summary: In this review paper we present recent results concerning the local eigenvalues statistics of non-selfadjoint one-dimensional semiclassical pseudo-differential operators subject to small random perturbations. We compare the eigenvalue statistics for perturbations by random matrix and by random potential. We show that they are universal in the sense that they only depend on the principal symbol of the operator and the type of perturbation and that they are independent of the distribution of the perturbation.
Moreover, we will outline the the proof of the principal results in the case of a model operator. The discussed results are [S. Nonnenmacher and M. Vogel, J. Eur. Math. Soc. (JEMS) 23, No. 5, 1521–1612 (2021; Zbl 1465.35323)].
Moreover, we will outline the the proof of the principal results in the case of a model operator. The discussed results are [S. Nonnenmacher and M. Vogel, J. Eur. Math. Soc. (JEMS) 23, No. 5, 1521–1612 (2021; Zbl 1465.35323)].
MSC:
| 35S05 | Pseudodifferential operators as generalizations of partial differential operators |
| 35P20 | Asymptotic distributions of eigenvalues in context of PDEs |
| 35-02 | Research exposition (monographs, survey articles) pertaining to partial differential equations |
Citations:
Zbl 1465.35323Software:
EigtoolReferences:
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