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

Journal of Statistical Physics volume 140, pages 268–288 (2010)Cite this article

Abstract

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. Our argument also applies to restricted trace ensembles with monomial potentials. In addition, by using the universal result in the bulk for fixed trace Gaussian unitary ensemble, which has been obtained by Götze and Gordin, we also prove the universal limits of correlation functions everywhere in the bulk for bounded trace Gaussian unitary ensemble.

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Authors and Affiliations

  1. School of Mathematical Sciences, Peking University, Beijing, 100871, P.R. China

    Dang-Zheng Liu

  2. Department of Mathematics, University of Macau, Av. Padre Tomás Pereira, Taipa, Macau, P.R. China

    Da-Sheng Zhou

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  1. Dang-Zheng Liu
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  2. Da-Sheng Zhou
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Correspondence to Dang-Zheng Liu.

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Liu, DZ., Zhou, DS. Some Universal Properties for Restricted Trace Gaussian Orthogonal, Unitary and Symplectic Ensembles. J Stat Phys 140, 268–288 (2010). https://doi.org/10.1007/s10955-010-9993-9

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  • DOI: https://doi.org/10.1007/s10955-010-9993-9

Keywords

  • Fixed trace ensembles
  • Bounded trace ensembles
  • Universality