发表机构
Seoul National University; Hokkaido University（首尔大学; 北海道大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
基于$q$-CCR代数表示论构造$q$-变形多解析Fock空间及相应点过程，证明粒子数和$q$同时趋于极限时线性统计量的中心极限定理，且重标度后协方差与经典情形一致。
AI 中文摘要
基于$q$-CCR代数的表示论，我们发展了一种表示论构造方法，用于构建$q$-变形多解析Fock空间、其再生核以及相关的$q$-变形多解析Bargmann变换。相关的行列式点过程提供了纯多解析和完全多解析Ginibre系综的$q$-变形。此外，我们确定了它们的极限密度，并建立了当粒子数趋于无穷且变形参数$q$同时趋于1时，其线性统计量波动的中心极限定理。值得注意的是，尽管$q$-变形改变了宏观密度和液滴的大小，但在空间重标度后，极限协方差结构与经典多解析Ginibre系综的相一致。
英文摘要
Based on the representation theory of the $q$-CCR algebra, we develop a representation-theoretic construction of the $q$-deformed polyanalytic Fock spaces, their reproducing kernels, and the associated $q$-deformed polyanalytic Bargmann transforms. The associated determinantal point processes provide $q$-deformations of the pure and full polyanalytic Ginibre ensembles. Moreover, we determine their limiting density and establish central limit theorems for the fluctuations of their linear statistics as the number of particles tends to infinity and the deformation parameter $q$ tends to 1 simultaneously. Remarkably, although the $q$-deformation changes the macroscopic density and the size of the droplet, the limiting covariance structures coincide, after spatial rescaling, with those of the classical polyanalytic Ginibre ensembles.
Comments37 pages
