Hyperuniformity of the determinantal point processes associated with the Heisenberg group
Hyperuniformity of the determinantal point processes associated with the Heisenberg group
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发表时间：
2022-03
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通讯作者：
M. Katori
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作者：
M. Katori
Ginibre点过程是由非厄米复高斯矩阵的特征值分布在无限矩阵大小的限制。这是复平面C上的一个行列式点过程（DPP），因为所有相关函数都是由称为相关核的积分核指定的行列式给出的。Shirai引入了Ginibre DPP的单参数（m ∈ N0）扩张，并称之为Ginibre型点过程。在本文中，我们考虑将C上的Ginibre和Ginibre型点过程推广到高维空间CD中的DPP，D = 2，3，. . .其中它们由多元水平m ∈ N0参数化。我们称所得到的点过程为扩展的海森堡DPP族，因为相关核通常等同于由薛定谔表示表示的海森堡群空间中两点的相关。我们证明了这个大家族中的所有DPP都是超均匀的I类。
The Ginibre point process is given by the eigenvalue distribution of a nonhermitian complex Gaussian matrix in the infinite matrix-size limit. This is a determinantal point process (DPP) on the complex plane C in the sense that all correlation functions are given by determinants specified by an integral kernel called the correlation kernel. Shirai introduced the one-parameter (m ∈ N0) extensions of the Ginibre DPP and called them the Ginibre-type point processes. In the present paper we consider a generalization of the Ginibre and the Ginibre-type point processes on C to the DPPs in the higher-dimensional spaces, CD,D = 2, 3, . . . , in which they are parameterized by a multivariate level m ∈ N0 . We call the obtained point processes the extended Heisenberg family of DPPs, since the correlation kernels are generally identified with the correlations of two points in the space of Heisenberg group expressed by the Schrödinger representations. We prove that all DPPs in this large family are in Class I of hyperuniformity.