Geodesic
On universality of bulk local regime of the deformed Gaussian Unitary Ensemble
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 5 (2009), pp. 396-433.

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T. Shcherbina. On universality of bulk local regime of the deformed Gaussian Unitary Ensemble. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 5 (2009), pp. 396-433. http://geodesic.mathdoc.fr/item/JMAG_2009_5_a5/

[1] 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

[2] L. Pastur, M. Shcherbina, “Universality of the Local Eigenvalue Statistics for a Class of Unitary Invariant Random Matrix Ensembles”, J. Stat. Phys., 86 (1997), 109–147 | DOI | MR | Zbl

[3] L. Pastur, M. Shcherbina, “Bulk Universality and Related Properties of Hermitian Matrix Model”, J. Stat. Phys., 130:2 (2007), 205–250 | DOI | MR

[4] L. Pastur, “The Spectrum of Random Matrices”, Teoret. Mat. Fiz., 10 (1972), 102–112 (Russian) | MR

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

[6] E. Brezin, S. Hikami, “Correlation of Nearby Levels Induced by a Random Potential”, Nucl. Phys., B479 (1996), 697–706 | DOI | MR | Zbl

[7] E. Brezin, S. Hikami, “Extension of Level-Spacing Universality”, Phys. Rev. E, 56 (1997), 264–269 | DOI | MR

[8] E. Brezin, S. Hikami, “Level Spacing of Random Matrices in an External Source”, Phys. Rev. E, 58 (1998), 7176–7185 | DOI | MR

[9] K. Johansson, “Universality of the Local Spacing Distribution in Certain Ensembles of Hermitian Wigner Matrices”, Commun. Math. Phys., 215 (2001), 683–705 | DOI | MR | Zbl

[10] P. M. Bleher, A. B. J. Kuijlaars, “Large $n$ Limit of Gaussian Random Matrices with External Source, I”, Commun. Math. Phys., 252 (2004), 43–76 | DOI | MR | Zbl

[11] A. I. Aptekarev, P. M. Bleher, A. B. J. Kuijlaars, “Large $n$ Limit of Gaussian Random Matrices with External Source, II”, Commun. Math. Phys., 25 (2005), 367–389 | DOI | MR

[12] G. Polya, G. Szego, Problems and Theorems in Analysis, Die Grundlehren der Math., II, Springer-Verlag, Wissenschaften, 1976

[13] N. I. Akhiezer, I. M. Glazman, Theory of Linear Operators in Hilbert Space, Dover, New York, 1993 | MR | Zbl

[14] R. Courant, D. Hilbert, Methods of Mathematical Physics, v. I, Interscience, New York, 1953 | MR

[15] L. Pastur, “A Simple Approach to the Global Regime of Gaussian Ensembles of Random Matrices”, Ukr. Math. J., 57 (2005), 936–966 | DOI | MR | Zbl

[16] M. A. Lavrentjev, B. V. Shabat, Methods of Theory of Functions of a Complex Variable, Russian, Nauka, Moscow, 1987