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Abstract: We give a proof of universality in the bulk of spectrum of unitary matrixmodels, assuming that the potential is globally $C^{2}$ and locally $C^{3}$function. The proof is based on the determinant formulas for correlationfunctions in terms of polynomials orthogonal on the unit circle. We do not useasymptotics of orthogonal polynomials. We obtain the $sin$-kernel as a uniquesolution of a certain non-linear integro-differential equation.



Author: Mihail Poplavskyi

Source: https://arxiv.org/







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