论文标题
与海森堡组相关的确定点过程的超均匀性
Hyperuniformity of the determinantal point processes associated with the Heisenberg group
论文作者
论文摘要
Ginibre点过程是通过在无限基质大小极限中的非甲米复合物矩阵的特征值分布给出的。这是复杂平面$ {\ mathbb {c}} $上的确定点过程（DPP），因为所有相关函数均由由称为相关内核的积分内核指定的确定剂给出。 Shirai引入了单参数（$ m \ in {\ Mathbb {n}} _ 0 $）Ginibre DPP的扩展，并将其称为Ginibre-type点过程。在本文中，我们考虑了$ {\ Mathbb {c}} $在$ {\ mathbb {c}} $上对DPP的概括的概括，并在较高的空间中向DPPS进行了概括，$ {\ Mathbb {c}}^d，d = 2,3，\ dots $，因为它们是由它们参数commutiativ in Multiv in commitiv in cam {\ mathbb {n}} _ 0^d $。我们称获得的点过程为扩展的Heisenberg DPP家族，因为通常在Heisenberg Group在Schrödinger代表表达的Heisenberg Group中的两个点的相关性通常鉴定出相关内核。我们证明，这个大家庭中的所有DPP都处于I级超均匀性。
The Ginibre point process is given by the eigenvalue distribution of a non-hermitian complex Gaussian matrix in the infinite matrix-size limit. This is a determinantal point process (DPP) on the complex plane ${\mathbb{C}}$ 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 ($m \in {\mathbb{N}}_0$) 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 ${\mathbb{C}}$ to the DPPs in the higher-dimensional spaces, ${\mathbb{C}}^D, D=2,3, \dots$, in which they are parameterized by a multivariate level $m \in {\mathbb{N}}_0^D$. 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.
