On Universality of Bulk Local Regime of the Deformed Gaussian Unitary Ensemble

Автор(и)

  • T. Shcherbina B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine, 47 Lenin Ave., Kharkiv, 61103, Ukraine

Ключові слова:

random matrices, universality, Gaussian Unitary Ensemble

Анотація

We consider the deformed Gaussian Ensemble $H_n=H_n^{(0)}+M_n$ in which $H_n^{(0)}$ is a hermitian matrix (possibly random) and $M_n$ is the Gaussian Unitary Ensemble (GUE) random matrix (independent of $H_n^{(0)}$ ). Assuming that the Normalized Counting Measure of $H_n^{(0)}$ converges weakly (in probability) to a nonrandom measure$N^{(0)}$ with a bounded support, we prove the universality of the local eigenvalue statistics in the bulk of the limiting spectrum of $H_n$.

Mathematics Subject Classification: 15A52, 15A57.

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(1)
Shcherbina, T. On Universality of Bulk Local Regime of the Deformed Gaussian Unitary Ensemble. Журн. мат. фіз. анал. геом. 2009, 5, 396-433.

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