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arXiv · 2112.04455

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

Mariya Shcherbina·Tatyana Shcherbina
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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

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Mariya Shcherbina, Tatyana Shcherbina. 2021-12-08. Finite-rank complex deformations of random band matrices: sigma-model approximation. https://arxiv.org/abs/2112.04455

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