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

@article{Nakano2019PoissonSF,
  title={Poisson Statistics for Beta Ensembles on the Real Line at High Temperature},
  author={F. Nakano and Khanh Duy Trinh},
  journal={Journal of Statistical Physics},
  year={2019},
  volume={179},
  pages={632-649}
}
This paper studies beta ensembles on the real line in a high temperature regime, that is, the regime where $$\beta N \rightarrow const \in (0, \infty )$$ β N → c o n s t ∈ ( 0 , ∞ ) , with N the system size and $$\beta $$ β 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… Expand
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