On Universality of Bulk Local Regime of the Deformed Gaussian Unitary Ensemble
Ключові слова:
random matrices, universality, Gaussian Unitary EnsembleАнотація
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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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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