Finite-Range Coulomb Gas Models I: Some Analytical Results
Statistical Mechanics
2020-03-04 v1 Mathematical Physics
math.MP
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 (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.
Keywords
Cite
@article{arxiv.1905.10524,
title = {Finite-Range Coulomb Gas Models I: Some Analytical Results},
author = {Akhilesh Pandey and Avanish Kumar and Sanjay Puri},
journal= {arXiv preprint arXiv:1905.10524},
year = {2020}
}