Power-law eigenvalue density, scaling, and critical random-matrix ensembles
Power-law eigenvalue density, scaling, and critical random-matrix ensembles
We consider a class of rotationally invariant unitary random matrix ensembles where the eigenvalue density falls off as an inverse power law. Under a 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 …