Random Matrices with Equispaced External Source
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Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. In: National Bureau of Standards Applied Mathematics Series, Vol. 55. For sale by the Superintendent of Documents. Washington, D.C.: U.S. Government Printing Office, 1964
Adler M., Delépine J., van Moerbeke P.: Dyson’s nonintersecting Brownian motions with a few outliers. Comm. Pure Appl. Math. 62(3), 334–395 (2009)
Adler M., Orantin N., van Moerbeke P.: Universality for the Pearcey process. Phys. D 239(12), 924–941 (2010)
Adler M., van Moerbeke P.: PDEs for the Gaussian ensemble with external source and the Pearcey distribution. Comm. Pure Appl. Math. 60(9), 1261–1292 (2007)
Aptekarev A.I., Bleher P.M., Kuijlaars A.B.J.: Large n limit of Gaussian random matrices with external source. II. Commun. Math. Phys. 259(2), 367–389 (2005)
Aptekarev A.I., Lysov V.G., Tulyakov D.N.: Random matrices with an external source and the asymptotics of multiple orthogonal polynomials. Mat. Sb. 202(2), 3–56 (2011)
Bai, Z., Silverstein, J.W.: Spectral analysis of large dimensional random matrices. In: Springer Series in Statistics, 2nd edn. New York: Springer, 2010
Baik J., Ben Arous G., Péché S.: Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices. Ann. Probab. 33(5), 1643–1697 (2005)
Baik J., Wang D.: On the largest eigenvalue of a Hermitian random matrix model with spiked external source I. Rank 1 case. Int. Math. Res. Not. IMRN 22, 5164–5240 (2011)
Baik J., Wang D.: On the largest eigenvalue of a hermitian random matrix model with spiked external source II Higher rank cases. Int. Math. Res. Not. IMRN 14, 3304–3370 (2013)
Bertola M., Buckingham R., Lee S., Pierce V.U.: Spectra of random Hermitian matrices with a small-rank external source: the supercritical and subcritical regimes. J. Stat. Phys. 153(4), 654–697 (2013)
Bertola M., Buckingham R., Lee S., Pierce V.U.: Spectra of random Hermitian matrices with a small-rank external source: the critical and near-critical regimes. J. Stat. Phys. 146(3), 475–518 (2012)
Bleher P., Delvaux S., Kuijlaars A.B.J.: Random matrices model with external source and a constrained vector equilibrium problem. Comm. Pure Appl. Math. 64(1), 116–160 (2011)
Bleher P., Kuijlaars A.B.J.: Large n limit of Gaussian random matrices with external source. I. Commun. Math. Phys. 252(1-3), 43–76 (2004)
Bleher P.M., Kuijlaars A.B.J.: Random matrices with external source and multiple orthogonal polynomials. Int. Math. Res. Not. 3, 109–129 (2004)
Bleher P.M., Kuijlaars A.B.J.: Integral representations for multiple Hermite and multiple Laguerre polynomials. Ann. Inst. Fourier (Grenoble) 55(6), 2001–2014 (2005)
Bleher P.M., Kuijlaars A.B.J.: Large n limit of Gaussian random matrices with external source. III. Double scaling limit. Commun. Math. Phys. 270(2), 481–517 (2007)
Brézin, E., Hikami, S.: Level spacing of random matrices in an external source. Phys. Rev. E (3), 58(6, part A), 7176–7185 (1998)
Conway, J.B.: Functions of one complex variable. II. In: Graduate Texts in Mathematics, Vol. 159, New York: Springer, 1995
Deift P., Kriecherbauer T., McLaughlin K.T.-R., Venakides S., Zhou X.: 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(11), 1335–1425 (1999)
Deift, P.A.: Orthogonal polynomials and random matrices: a Riemann–Hilbert approach. In: Courant Lecture Notes in Mathematics, Vol. 3, New York: New York University Courant Institute of Mathematical Sciences, 1999
El Karoui N.: Tracy-Widom limit for the largest eigenvalue of a large class of complex sample covariance matrices. Ann. Probab. 35(2), 663–714 (2007)
Eynard, B., Orantin, N.: Topological recursion in enumerative geometry and random matrices. J. Phys. A 42(29), 293001, 117 (2009)
Fokas A.S., Its A.R., Kitaev A.V.: The isomonodromy approach to matrix models in 2D quantum gravity. Commun. Math. Phys. 147(2), 395–430 (1992)
Gakhov, F.D.: Boundary value problems. New York: Dover Publications Inc., 1990. Translated from the Russian, Reprint of the 1966 translation, 1990
Johansson K.: On fluctuations of eigenvalues of random Hermitian matrices. Duke Math. J. 91(1), 151–204 (1998)
Johansson K.: Determinantal processes with number variance saturation. Commun. Math. Phys. 252(1-3), 111–148 (2004)
Nikishin, E.M., Sorokin, V.N.: Rational approximations and orthogonality. Translations of Mathematical Monographs, Vol. 92. Providence: American Mathematical Society, 1991. Translated from the Russian by Ralph P. Boas
Van Assche, W., Coussement, E.: Some classical multiple orthogonal polynomials. J. Comput. Appl. Math. 127(1–2), 317–347 (2001) (Numerical analysis 2000, Vol. V, Quadrature and orthogonal polynomials)
Van Assche, W., Geronimo, J.S., Kuijlaars, A.B.J.: Riemann–Hilbert problems for multiple orthogonal polynomials. In: Special Functions 2000: Current Perspective and Future Directions (Tempe, AZ), Vol. 30, NATO Sci. Ser. II Math. Phys. Chem. Dordrecht: Kluwer Academic Publishers, 2001, pp. 23–59