Free Random Levy Matrices
Abstract
Using the theory of free random variables (FRV) and the Coulomb gas analogy, we construct stable random matrix ensembles that are random matrix generalizations of the classical onedimensional stable Lévy distributions. We show that the resolvents for the corresponding matrices obey transcendental equations in the large size limit. We solve these equations in a number of cases, and show that the eigenvalue distributions exhibit Lévy tails. For the analytically known Lévy measures we explicitly construct the density of states using the method of orthogonal polynomials. We show that the Lévy taildistributions are characterized by a novel form of microscopic universality.
 Publication:

arXiv eprints
 Pub Date:
 November 2000
 arXiv:
 arXiv:condmat/0011451
 Bibcode:
 2000cond.mat.11451B
 Keywords:

 Mesoscopic Systems and Quantum Hall Effect
 EPrint:
 5 pages