  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 (FRCG) 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
new universality classes of random matrix ensembles. They also provide a
theoretical framework to study banded random matrices, and dynamical systems
whose matrix representation can be written in the form of banded matrices.
