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Poisson Statistics for Beta Ensembles on the Real Line at High Temperature

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Abstract

This paper studies beta ensembles on the real line in a high temperature regime, that is, the regime where \(\beta N \rightarrow const \in (0, \infty )\), with N the system size and \(\beta \) the inverse temperature. For the global behavior, the convergence to the equilibrium measure is a consequence of a recent result on large deviation principle. This paper focuses on the local behavior and shows that the local statistics around any fixed reference energy converges weakly to a homogeneous Poisson point process.

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Acknowledgements

This work is supported by JSPS KAKENHI Grant Number JP19K14547 (K.D.T.). The authors would like to thank the referees for many helpful suggestions.

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  1. Fumihiko Nakano

    Present address: Mathematical Institute, Tohoku University, Sendai, Japan

Authors and Affiliations

  1. Department of Mathematics, Gakushuin University, Tokyo, Japan

    Fumihiko Nakano

  2. Global Center for Science and Engineering, Waseda University, Tokyo, Japan

    Khanh Duy Trinh

Authors
  1. Fumihiko Nakano
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  2. Khanh Duy Trinh
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Correspondence to Khanh Duy Trinh.

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Communicated by Eric A. Carlen.

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Nakano, F., Trinh, K.D. Poisson Statistics for Beta Ensembles on the Real Line at High Temperature. J Stat Phys 179, 632–649 (2020). https://doi.org/10.1007/s10955-020-02542-y

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