• DOI:10.1103/PhysRevE.54.210
• Corpus ID: 11636250

Theory of random matrices with strong level confinement: Orthogonal polynomial approach.

@article{Freilikher1996TheoryOR,
  title={Theory of random matrices with strong level confinement: Orthogonal polynomial approach.},
  author={Freilikher and Kanzieper and Yurkevich},
  journal={Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics},
  year={1996},
  volume={54 1},
  pages={
          210-219
        }
}

• Freilikher, Kanzieper, Yurkevich
• Published 2 October 1995
• Mathematics
• Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

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.