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 correlations. We show that such ensembles belong to the class of critical ensembles.
Muttalib
K A
KA
Department of Physics, University of Florida, P.O. Box 118440, Gainesville, Florida 32611-8440, USA. muttalib@phys.ufl.edu
Ismail
Mourad E H
ME