Finite-Rank Complex Deformations of Random Band Matrices: Sigma-Model Approximation

Автор(и)

  • Mariya Shcherbina B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine, 47 Nauky Ave., Kharkiv, 61103, Ukraine
  • Tatyana Shcherbina Department of Mathematics, University of Wisconsin–Madison, 480 Linkoln Drive, Madison, WI 53706, USA

DOI:

https://doi.org/10.15407/mag19.01.211

Ключові слова:

випадковi стрiчковi матрицi, делокалiзований режим, комплексна деформацiя, сiгма-модель, суперсиметрiя

Анотація

Ми вивчаємо розподiл комплексних власних значень $z_1, \ldots , z_N$ випадкової ермiтової блокової стрiчкової матрицi розмiру N×N з комплексною деформацiєю скiнченного рангу. У режимi, коли розмiр блоков $W$ зростає швидше за $\sqrt{N}$, ми доводимо, що гранична щiльнiсть $\Im z_1, \ldots , \Im z_N$ у сiгма-модельнiй апроксимацiї збiгається з вiдповiдною щiльнiстю для Ґаусiвського унiтарного ансамблю. Для цього ми використовуємо метод, розроблений в [16].

Mathematical Subject Classification 2020: 60B20

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Shcherbina, M.; Shcherbina, T. Finite-Rank Complex Deformations of Random Band Matrices: Sigma-Model Approximation. Журн. мат. фіз. анал. геом. 2023, 19, 211-246.

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