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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}
}