Power law eigenvalue density, scaling and critical random matrix ensembles

Details Power law eigenvalue density, scaling and critical random matrix ensembles Power law eigenvalue density, scaling and critical random matrix ensembles

2007-10-24

arxiv.org/abs/0710.4527v1

Physics

Condensed Matter

Statistical Mechanics

to be published in Phys. Rev. E

Scientific paper

10.1103/PhysRevE.76.051105

We consider a class of rotationally invariant unitary random matrix ensembles where the eigenvalue density falls off as an inverse power law. Under a new scaling appropriate for such power law densities (different from the scaling required in Gaussian random matrix ensembles), we calculate exactly the two-level kernel that determines all eigenvalue correlations. We show that such ensembles belong to the class of critical ensembles.

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