Theory of random matrices with strong level confinement
Abstract
Unitary ensembles of large N x N random matrices with a non-Gaussian probability distribution P[H] ~ exp{-TrV[H]} are studied using a theory of polynomials orthogonal with respect to exponential weights. Asymptotically exact expressions for density of levels, one- and two-point Green's functions are calculated. We show that in the large-N limit the properly rescaled local eigenvalue correlations are independent of P[H] while global smoothed connected correlations depend on P[H] only through the endpoints of spectrum. We also establish previously unknown intimate connection between structure of Szeg\"o function entering strong polynomial asymptotics and mean-field equation by Dyson.
Cite
@article{arxiv.cond-mat/9510002,
title = {Theory of random matrices with strong level confinement},
author = {V. Freilikher and E. Kanzieper and I. Yurkevich},
journal= {arXiv preprint arXiv:cond-mat/9510002},
year = {2008}
}
Comments
4 pages (latex), Several misprints corrected. Extended version available at cond-mat/9604078