Dyson has shown an equivalence between infinite-range Coulomb gas models and classical random matrix ensembles for the study of eigenvalue statistics. In this paper, we introduce finite-range Coulomb gas models as a generalization of the Dyson models with a finite range of eigenvalue interactions. As the range of interaction increases, there is a transition from Poisson statistics to classical random matrix statistics. These models yield distinct universality classes of random matrix ensembles. They also provide a theoretical framework to study banded random matrices, and dynamical systems the matrix representation of which can be written in the form of banded matrices.

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有限范围的库仑气体模型。一，部分分析结果

戴森（Dyson）显示了无限范围的库仑气体模型与经典随机矩阵集成之间的等效性，用于特征值统计的研究。在本文中，我们引入有限范围的库仑气体模型，作为具有有限范围特征值相互作用的戴森模型的推广。随着交互作用范围的增加，从泊松统计量向经典随机矩阵统计量过渡。这些模型产生随机矩阵集合的不同通用性类别。它们还提供了研究带状随机矩阵和动力学系统的理论框架，其矩阵表示可以以带状矩阵的形式编写。