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

  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},
  volume={54 1},
  • 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… 
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