Poisson Statistics for Beta Ensembles on the Real Line at High Temperature
Poisson Statistics for Beta Ensembles on the Real Line at High Temperature
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DOI：
10.1007/s10955-020-02542-y
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发表时间：
2020-04
影响因子：
1.6
通讯作者：
Fumihiko Nakano;Khanh Duy Trinh
中科院分区：
文献类型：
--
作者：
Fumihiko Nakano;Khanh Duy Trinh
本文研究高温状态下实线上的β系综，即其中，系统尺寸N和温度的倒数。对于全局行为，向均衡度量的收敛是大偏差原理的最新结果的结果。本文重点关注局部行为，并表明任何固定参考能量周围的局部统计量都弱收敛于齐次泊松点过程。
This paper studies beta ensembles on the real line in a high temperature regime, that is, the regime where, withNthe system size andthe 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.