Abstract
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.
- Received 29 July 2019
- Accepted 31 January 2020
DOI:https://doi.org/10.1103/PhysRevE.101.022217
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