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We consider asymptotics of orthogonal polynomial ensembles, in the macroscopic and mesoscopic scales.
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P. Deift, T. Kriecherbauer, K.T.-R. McLaughlin, S. Venakides, and X. Zhou, Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory , Comm. Pure Appl. Math. 52
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P. Deift, T. Kriecherbauer, K.T.-R. McLaughlin, S. Venakides, and X. Zhou, Strong asymptotics for polynomials orthogonal with respect to varying exponential weights , Comm. Pure Appl. Math. 52
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D. Lubinsky, A new approach to universality involving orthogonal polynomials
2009
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D. Lubinsky Some recent methods for establishing universality limits
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2002
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R. Lyons, Determinantal probability measures , Publ. Math. Inst. Hautes Etudes Sci. 98
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W. König, Orthogonal polynomial ensembles in probability theory , Probab. Surveys 2
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J. B. Hough, M. Krishnapur, Y. Peres and B. Virág, Determinantal processes and independence , Prob. Surv. 3
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A. Soshnikov, Determinantal random point fields, in: Encyclopedia of Mathematical Physics, 47–53. Oxford: Elsevier, 2006
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B. Simon, Weak convergence of CD kernels and applications
2009
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V. Totik, Universality and fine zero spacing on general sets
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D. Lubinsky, A maximal function approach to Christoffel functions and Nevai operators , Constr. Approx. 34
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L. Erdős and H.-T. Yau, Universality of local spectral statistics of random matrices , Bull. Amer. Math. Soc. 49
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