Power law eigenvalue density, scaling and critical random matrix ensembles
Statistical Mechanics
2009-11-13 v1 Disordered Systems and Neural Networks
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.
Cite
@article{arxiv.0710.4527,
title = {Power law eigenvalue density, scaling and critical random matrix ensembles},
author = {K. A. Muttalib and Mourad E. H. Ismail},
journal= {arXiv preprint arXiv:0710.4527},
year = {2009}
}
Comments
to be published in Phys. Rev. E