论文标题
确定点过程和费米昂准式状态
Determinantal point processes and fermion quasifree states
论文作者
论文摘要
确定点过程的特征是相关函数的特殊结构特性：它们由相关内核的未成年人给出。但是，与相关函数本身不同，该内核不是本质上定义的，并且许多不同的内核可以生成相同的确定过程。相关内核的非唯一性在研究确定过程中造成困难。 我们提出了一种形式主义，该形式主义允许在某些其他假设下找到一个杰出的相关内核。这个想法是利用确定过程和准确态在典型反通信关系的代数上的准过程之间的联系。 我们证明，形式主义适用于离散的正交多项式组合，以及其一些大N限制，包括离散的正弦过程以及与离散的Hermite，Laguerre和Alexei Borodin和Alexei Borodin和[Commun In In commun In In commun in [Commun》中的Increstal Hermite和Jacobi内核的确定过程。数学。物理。 353（2017），853-903; ARXIV：1608.01564]。作为应用程序，我们解决了其中一些过程的等效/脱节二分法。
Determinantal point processes are characterized by a special structural property of the correlation functions: they are given by minors of a correlation kernel. However, unlike the correlation functions themselves, this kernel is not defined intrinsically, and the same determinantal process can be generated by many different kernels. The non-uniqueness of a correlation kernel causes difficulties in studying determinantal processes. We propose a formalism which allows to find a distinguished correlation kernel under certain additional assumptions. The idea is to exploit a connection between determinantal processes and quasifree states on CAR, the algebra of canonical anticommutation relations. We prove that the formalism applies to discrete N-point orthogonal polynomial ensembles and to some of their large-N limits including the discrete sine process and the determinantal processes with the discrete Hermite, Laguerre, and Jacobi kernels investigated by Alexei Borodin and the author in [Commun. Math. Phys. 353 (2017), 853-903; arXiv:1608.01564]. As an application we resolve the equivalence/disjointness dichotomy for some of those processes.
