Power law eigenvalue density, scaling and critical random matrix ensembles
arXiv:0710.4527 · doi:10.1103/PhysRevE.76.051105
Abstract
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.
to be published in Phys. Rev. E
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