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Central limit theorem for linear eigenvalue statistics of orthogonally invariant matrix models
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 4 (2008) no. 1, pp. 171-195 Cet article a éte moissonné depuis la source Math-Net.Ru

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We prove central limit theorem for linear eigenvalue statistics of orthogonally invariant ensembles of random matrices with one interval limiting spectrum. We consider ensembles with real analytic potentials and test functions with two bounded derivatives. 
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M. Shcherbina. Central limit theorem for linear eigenvalue statistics of orthogonally invariant matrix models. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 4 (2008) no. 1, pp. 171-195. http://geodesic.mathdoc.fr/item/JMAG_2008_4_1_a8/

[1] S. Albeverio, L. Pastur, M. Shcherbina, “On Asymptotic Properties of Certain Orthogonal Polynomials”, Mat. fiz., analiz, geom., 4 (1997), 263–277 | MR | Zbl

[2] S. Albeverio, L. Pastur, M. Shcherbina, “On the $1/n$ Expansion for Some Unitary Invariant Ensembles of Random Matrices”, Commun. Math. Phys., 224 (2001), 271–305 | DOI | MR | Zbl

[3] A. Boutet de Monvel, L. Pastur, M. Shcherbina, “On the Statistical Mechanics Approach in the Random Matrix Theory. Integrated Density of States”, J. Stat. Phys., 79 (1995), 585–611 | DOI | MR | Zbl

[4] P. Deift, T. Kriecherbauer, K. McLaughlin, S. Venakides, X. Zhou, “Uniform Asymptotics for Polynomials Orthogonal with Respect to Varying Exponential Weights and Applications to Universality Questions in Random Matrix Theory”, Commun. Pure Appl. Math., 52 (1999), 1335–1425 | 3.0.CO;2-1 class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | MR | Zbl

[5] P. Deift, T. Kriecherbauer, K. McLaughlin, S. Venakides, X. Zhou, “Strong Asymptotics of Orthogonal Polynomials with Respect to Exponential Weights”, Commun. Pure Appl. Math., 52 (1999), 1491–1552 | 3.0.CO;2-%23 class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | MR | Zbl

[6] P. Deift, D. Gioev, Universality in Random Matrix Theory for Orthogonal and Symplectic Ensembles, preprint, arXiv: math-ph/0411075 | MR

[7] P. Deift, D. Gioev, Universality at the Edge of the Spectrum for Unitary, Orthogonal, and Symplectic Ensembles of Random Matrices, preprint, arXiv: math-ph/0507023 | MR

[8] K. Johansson, “On Fluctuations of Eigenvalues of Random Hermitian Matrices”, Duke Math. J., 91 (1998), 151–204 | DOI | MR | Zbl

[9] M. L. Mehta, Random Matrices, Acad. Press, New York, 1991 | MR | Zbl

[10] N. I. Muskhelishvili, Singular Integral Equations, P. Noordhoff., Groningen, 1953 | MR

[11] L. Pastur, “Limiting Laws of Linear Eigenvalue Statistics for Unitary Invariant Matrix Models”, J. Math. Phys., 47 (2006), 103303 | DOI | MR | Zbl