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Random matrices with equispaced external source

Bibliographic reference Claeys, Tom ; Wang, Dong. Random matrices with equispaced external source. In: Communications in Mathematical Physics, Vol. 328, no. 3, p. 1023-1077 (2014)
Permanent URL http://hdl.handle.net/2078.1/136106
  1. 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
  2. Adler Mark, Delépine Jonathan, van Moerbeke Pierre, Dyson's nonintersecting Brownian motions with a few outliers, 10.1002/cpa.20264
  3. Adler Mark, Orantin Nicolas, van Moerbeke Pierre, Universality for the Pearcey process, 10.1016/j.physd.2010.01.005
  4. Adler Mark, van Moerbeke Pierre, PDEs for the Gaussian ensemble with external source and the Pearcey distribution, 10.1002/cpa.20175
  5. Aptekarev Alexander I., Bleher Pavel M., Kuijlaars Arno B.J, Large n Limit of Gaussian Random Matrices with External Source, Part II, 10.1007/s00220-005-1367-9
  6. Аптекарев Александр Иванович, Aptekarev Alexander Ivanovich, Лысов Владимир Генрихович, Lysov Vladimir Genrikhovich, Туляков Дмитрий Николаевич, Tulyakov Dmitrii Nikolaevich, Случайные матрицы с внешним источником и асимптотика совместно ортогональных многочленов, 10.4213/sm7702
  7. Bai, Z., Silverstein, J.W.: Spectral analysis of large dimensional random matrices. In: Springer Series in Statistics, 2nd edn. New York: Springer, 2010
  8. Baik Jinho, Ben Arous Gérard, Péché Sandrine, Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices, 10.1214/009117905000000233
  9. 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)
  10. 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)
  11. Bertola M., Buckingham R., Lee S. Y., Pierce V., Spectra of Random Hermitian Matrices with a Small-Rank External Source: The Supercritical and Subcritical Regimes, 10.1007/s10955-013-0845-2
  12. Bertola M., Buckingham R., Lee S. Y., Pierce V., Spectra of Random Hermitian Matrices with a Small-Rank External Source: The Critical and Near-Critical Regimes, 10.1007/s10955-011-0409-2
  13. Bleher P., Delvaux S., Kuijlaars A. B. J., Random matrix model with external source and a constrained vector equilibrium problem, 10.1002/cpa.20339
  14. Bleher Pavel, Kuijlaars Arno B. J., Large n Limit of Gaussian Random Matrices with External Source, Part I, 10.1007/s00220-004-1196-2
  15. Bleher P., Kuijlaars A., , 10.1155/s1073792804132194
  16. M. BLEHER Pavel, B.J. Kuijlaars Arno, Integral representations for multiple Hermite and multiple Laguerre polynomials, 10.5802/aif.2148
  17. Bleher Pavel M., Kuijlaars Arno B. J., Large n Limit of Gaussian Random Matrices with External Source, Part III: Double Scaling Limit, 10.1007/s00220-006-0159-1
  18. Brézin, E., Hikami, S.: Level spacing of random matrices in an external source. Phys. Rev. E (3), 58(6, part A), 7176–7185 (1998)
  19. Conway John B., Functions of One Complex Variable II, ISBN:9781461269113, 10.1007/978-1-4612-0817-4
  20. 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, 10.1002/(sici)1097-0312(199911)52:11<1335::aid-cpa1>3.0.co;2-1
  21. 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
  22. El Karoui Noureddine, Tracy–Widom limit for the largest eigenvalue of a large class of complex sample covariance matrices, 10.1214/009117906000000917
  23. Eynard, B., Orantin, N.: Topological recursion in enumerative geometry and random matrices. J. Phys. A 42(29), 293001, 117 (2009)
  24. Fokas A. S., Its A. R., Kitaev A. V., The isomonodromy approach to matric models in 2D quantum gravity, 10.1007/bf02096594
  25. Gakhov, F.D.: Boundary value problems. New York: Dover Publications Inc., 1990. Translated from the Russian, Reprint of the 1966 translation, 1990
  26. Harish-Chandra, Differential Operators on a Semisimple Lie Algebra, 10.2307/2372387
  27. Itzykson C., Zuber J.‐B., The planar approximation. II, 10.1063/1.524438
  28. Johansson Kurt, On fluctuations of eigenvalues of random Hermitian matrices, 10.1215/s0012-7094-98-09108-6
  29. Johansson Kurt, Determinantal Processes with Number Variance Saturation, 10.1007/s00220-004-1186-4
  30. 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
  31. 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)
  32. 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
  33. Zinn-Justin P., Random Hermitian matrices in an external field, 10.1016/s0550-3213(97)00307-6