 9785 Pavel Bleher, Alexander Its
 Semiclassical Asymptotics of Orthogonal
Polynomials, RiemannHilbert Problem, and
Universality in the Matrix Model
(309K, TeX)
Feb 20, 97

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Abstract. We derive semiclassical asymptotics for the
orthogonal polynomials on the line with the weight $\exp(NV(z))$,
where $V(z)=\di{tz^2\over 2}+{gz^4\over 4},\;g>0,\;t<0$, is a
doublewell quartic polynomial. Simultaneously we derive semiclassical
asymptotics for the recursive coefficients of the orthogonal
polynomials. The proof of the asymptotics is based on the
analysis of the appropriate matrix RiemannHilbert problem. As an
application of the semiclassical asymptotics, we prove the universality
of the local distribution of eigenvalues in the matrix model with
the doublewell quartic interaction in the presence of two cuts.
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