固定迹$β$ -Hermite系综：渐近eigenvalue密度和密度的边缘
Fixed trace $β$-Hermite ensembles: Asymptotic eigenvalue density and the edge of the density
摘要：
在本文中，固定迹$β$ -Hermite系综推广固定迹高斯Hermite系综。对于所有的$β$，我们用两种不同的方法证明了这些系综的Wigner周期律：一种是借助于一般$β$的矩阵模型的矩等价方法，另一种是利用渐近分析工具.在边缘的密度，我们证明了边缘缩放极限$β$ -HE意味着相同的限制固定的跟踪$β$ -Hermite合奏。因此，可以给出固定迹GOE、GUE和GSE的显式极限。此外，对于甚至$β$，类似于$β$ -Hermite系综，可以获得Konstevich型的多重积分。
英文摘要：
In the present paper, fixed trace $β$-Hermite ensembles generalizing the fixed trace Gaussian Hermite ensemble are considered. For all $β$, we prove the Wigner semicircle law for these ensembles by using two different methods: one is the moment equivalence method with the help of the matrix model for general $β$, the other is to use asymptotic analysis tools. At the edge of the density, we prove that the edge scaling limit for $β$-HE implies the same limit for fixed trace $β$-Hermite ensembles. Consequently, explicit limit can be given for fixed trace GOE, GUE and GSE. Furthermore, for even $β$, analogous to $β$-Hermite ensembles, a multiple integral of the Konstevich type can be obtained.
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