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arXiv · 1905.10524

Finite-Range Coulomb Gas Models I: Some Analytical Results

Akhilesh Pandey·Avanish Kumar·Sanjay Puri
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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.

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BibTeXRIS

Akhilesh Pandey, Avanish Kumar, Sanjay Puri. 2019-05-25. Finite-Range Coulomb Gas Models I: Some Analytical Results. https://doi.org/10.1103/physreve.101.022217

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