Universal Cubic Eigenvalue Repulsion for Random Normal Matrices

Details Universal Cubic Eigenvalue Repulsion for Random Normal Matrices Universal Cubic Eigenvalue Repulsion for Random Normal Matrices

1996-10-08

arxiv.org/abs/cond-mat/9610073v1

Physics

Condensed Matter

Statistical Mechanics

15 pages, 2 eps figures. to appar in Physical Review E

Scientific paper

10.1103/PhysRevE.55.205

Random matrix models consisting of normal matrices, defined by the sole constraint $[N^{\dag},N]=0$, 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.

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