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Bulk universality for unitary matrix models
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 5 (2009) no. 3, pp. 245-274 Cet article a éte moissonné depuis la source Math-Net.Ru

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A proof of universality in the bulk of spectrum of unitary matrix models, assuming that the potential is globally $C^2$ and locally $C^3$ function (see Theorem 1.2), is given. The proof is based on the determinant formulas for correlation functions in terms of polynomials orthogonal on the unit circle. The sin-kernel is obtained as a unique solution of a certain nonlinear integrodifferential equation without using asymptotics of orthogonal polynomials. 
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M. Poplavskyi. Bulk universality for unitary matrix models. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 5 (2009) no. 3, pp. 245-274. http://geodesic.mathdoc.fr/item/JMAG_2009_5_3_a1/

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