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Semiclassical Asymptotics of Orthogonal Polynomials, Riemann-Hilbert Problem, and Universality in the Matrix Model
We derive semiclassical asymptotics for the orthogonal polynomials P n (z) on the line with respect to the exponential weight exp(-N V (z)), where V (z) is a double-well quartic polynomial, in the limit when n, N → ∞.We assume that ε ≤ (n/N ) ≤ λ cr -ε for …