Finite-rank complex deformations of random band matrices: sigma-model approximation

Mariya Shcherbina; Tatyana Shcherbina

Finite-rank complex deformations of random band matrices: sigma-model approximation

Mathematical Physics 2021-12-09 v1 math.MP

Authors: Mariya Shcherbina , Tatyana Shcherbina

Abstract

We study the distribution of complex eigenvalues $z_1,\ldots, z_N$ of random Hermitian $N\times N$ block band matrices with a complex deformation of a finite rank. Assuming that the width of the band $W$ grows faster than $\sqrt{N}$ , we proved that the limiting density of $\Im z_1,\ldots, \Im z_N$ in a sigma-model approximation coincides with that for the Gaussian Unitary Ensemble. The method follows the techniques of arXiv:1802.03813

Keywords

random matrix theory eigenvalue spectra

Cite

@article{arxiv.2112.04455,
  title  = {Finite-rank complex deformations of random band matrices: sigma-model approximation},
  author = {Mariya Shcherbina and Tatyana Shcherbina},
  journal= {arXiv preprint arXiv:2112.04455},
  year   = {2021}
}

Comments

30 pp. arXiv admin note: substantial text overlap with arXiv:1802.03813

Finite-rank complex deformations of random band matrices: sigma-model approximation

Abstract

Keywords

Cite

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