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We study orthogonal and symplectic matrix models with polynomial potentials and multi interval supports of the equilibrium measure.
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M.L.Mehta, M.L.: Random Matrices. New York: Academic Press, 1991
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Boutet de Monvel, A., Pastur L., Shcherbina M.: On the statistical mechanics approach in the random matrix theory. Integrated density of states. J. Stat. Phys
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Pastur, L., Shcherbina, M.: Universality of the local eigenvalue statistics for a class of unitary invariant random matrix ensembles. J. Stat. Phys
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Johansson, K.: On fluctuations of eigenvalues of random Hermitian matrices. Duke Math. J
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Deift, P., Kriecherbauer, T., McLaughlin, K., Venakides, S., Zhou, X.: Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory. Commun. Pure Appl. Math
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Widom, H.: On the relations between orthogonal, symplectic and unitary matrix models. J.Stat.Phys
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Kuijlaars, A.B.J., McLaughlin, A K. T-R Generic behavior of the density of states in random matrix theory and equilibrium problems in the presence of real analytic external fields, Comm. Pure Appl. Math
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Albeverio, S., Pastur, L., Shcherbina, M.: On the
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Stojanovic, A.: Universality in orthogonal and symplectic invariant matrix models with quatric potentials. Math.Phys.Anal.Geom
2002
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Bleher, P., Its, A. Double scaling limit in the random matrix model: the Riemann-Hilbert approach, Comm. Pure Appl. Math
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Ercolani N.M., McLaughlin K.D.: Asymptotics of the partition function for random matrices via Riemann-Hilbert techniques, and applications to graphical enumerations. Int.Math.Res.Not
2003
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Deift, P., Gioev, D.: Universality at the edge of the spectrum for unitary, orthogonal, and symplectic ensembles of random matrices Comm. Pure Appl. Math
2007
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Deift, P., Gioev, D., Kriecherbauer, T., Vanlessen, M.: Universality for orthogonal and symplectic Laguerre-type ensembles. J.Stat.Phys
2007
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Pastur, L., Shcherbina, M.: Bulk universality and related properties of Hermitian matrix models. J.Stat.Phys
2007
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Levin L.,Lubinskky D.S.: Universality limits in the bulk for varying measures. Adv. Math
2008
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Shcherbina, M.: Double scaling limit for matrix models with non analytic potentials. J. Math. Phys
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Claeys, T., Kuijalaars, A.B.J.: Universality of the double scaling limit in random matrix models, Comm. Pure Appl. Math
2006
Cited alongside, same era.
Deift, P., Gioev, D.: Universality in random matrix theory for orthogonal and symplectic ensembles. Int. Math. Res. Papers. 2007, 004-116
2007
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Kriecherbauer,T., Shcherbina, M.: Fluctuations of eigenvalues of matrix models and their applications. preprint arxive: math-ph/1003.6121
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Shcherbina, M.: On Universality for Orthogonal Ensembles of Random Matrices Commun.Math.Phys
2009
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Shcherbina, M.: Edge Universality for Orthogonal Ensembles of Random Matrices J.Stat.Phys (2009)
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