Semiclassical asymptotics of orthogonal polynomials , Riemann-Hilbert problem , and universality in the matrix model

@inproceedings{Bleher1999SemiclassicalAO,
  title={Semiclassical asymptotics of orthogonal polynomials , Riemann-Hilbert problem , and universality in the matrix model},
  author={By Pavel Bleher},
  year={1999}
}
  • By Pavel Bleher
  • Published 1999
We derive semiclassical asymptotics for the orthogonal polynomials Pn(z) on the line with respect to the exponential weight exp(-NV(z)), where V(z) is a double-well quartic polynomial, in the limit when n, N -+ oo. We assume that E < (n/N) < Acr E for some e > 0, where Acr is the critical value which separates orthogonal polynomials with two cuts from the ones with one cut. Simultaneously we derive semiclassical asymptotics for the recursive coefficients of the orthogonal polynomials, and we… CONTINUE READING
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