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Dyson demonstrated an equivalence between infinite-range Coulomb gas modelsand classical random matrix ensembles for study of eigenvalue statistics. Weintroduce finite-range Coulomb gas (FRCG) models via a Brownian matrix process,and study them analytically and by Monte-Carlo simulations. These models yieldnew universality classes, and provide a theoretical framework for study ofbanded random matrices (BRM) and quantum kicked rotors (QKR). We demonstratethat, for a BRM of bandwidth b and a QKR of chaos parameter {\alpha}, theappropriate FRCG model has the effective range d = (b^2)/N = ({\alpha}^2)/N,for large N matrix dimensionality. As d increases, there is a transition fromPoisson to classical random matrix statistics.

Finite-Range Coulomb Gas Models of Banded Random Matrices and Quantum Kicked Rotors