Universal Cubic Eigenvalue Repulsion for Random Normal Matrices
Statistical Mechanics
2009-10-28 v1
Abstract
Random matrix models consisting of normal matrices, defined by the sole constraint , will be explored. It is shown that cubic eigenvalue repulsion in the complex plane is universal with respect to the probability distribution of matrices. The density of eigenvalues, all correlation functions, and level spacing statistics are calculated. Normal matrix models offer more probability distributions amenable to analytical analysis than complex matrix models where only a model wth a Gaussian distribution are solvable. The statistics of numerically generated eigenvalues from gaussian distributed normal matrices are compared to the analytical results obtained and agreement is seen.
Cite
@article{arxiv.cond-mat/9610073,
title = {Universal Cubic Eigenvalue Repulsion for Random Normal Matrices},
author = {Gary Oas},
journal= {arXiv preprint arXiv:cond-mat/9610073},
year = {2009}
}
Comments
15 pages, 2 eps figures. to appar in Physical Review E