Unitary random-matrix ensemble with governable level confinement.

  title={Unitary random-matrix ensemble with governable level confinement.},
  author={Freilikher and Kanzieper and Yurkevich},
  journal={Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics},
  volume={53 3},
  • Freilikher, Kanzieper, Yurkevich
  • Published 2 October 1995
  • Mathematics, Medicine, Physics
  • Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
A family of unitary \ensuremath{\alpha} ensembles of random matrices with governable confinement potential V(x)\ensuremath{\sim}\ensuremath{\Vert}x${\mathrm{\ensuremath{\Vert}}}^{\mathrm{\ensuremath{\alpha}}}$ is studied employing exact results of the theory of nonclassical orthogonal polynomials. The density of levels, two-point kernel, locally rescaled two-level cluster function, and smoothed connected correlations between the density of eigenvalues are calculated for strong (\ensuremath… 
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