Some Universal Properties for Restricted Trace Gaussian Orthogonal, Unitary and Symplectic Ensembles

Details Some Universal Properties for Restricted Trace Gaussian Orthogonal, Unitary and Symplectic Ensembles Some Universal Properties for Restricted Trace Gaussian Orthogonal, Unitary and Symplectic Ensembles

2009-05-29

arxiv.org/abs/0905.4932v2

Physics

Mathematical Physics

19pages,bounded trace Gaussian ensembles are added

Scientific paper

Consider fixed and bounded trace Gaussian orthogonal, unitary and symplectic ensembles, closely related to Gaussian ensembles without any constraint. For three restricted trace Gaussian ensembles, we prove universal limits of correlation functions at zero and at the edge of the spectrum edge. In addition, by using the universal result in the bulk for fixed trace Gaussian unitary ensemble, which has been obtained by G$\ddot{o}$tze and Gordin, we also prove universal limits of correlation functions for bounded trace Gaussian unitary ensemble.

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