# Hankel Determinant and Orthogonal Polynomials for a Gaussian Weight with a Discontinuity at the Edge

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Bibliographic reference Bogatskiy, Alexander ; Claeys, Tom ; Its, Alexander R. Hankel Determinant and Orthogonal Polynomials for a Gaussian Weight with a Discontinuity at the Edge. In: Communications in Mathematical Physics, Vol. 347, no.1, p. 127-162 (23/06/2016) http://hdl.handle.net/2078.1/181830
1. Ablowitz M. J., Segur H., Asymptotic Solutions of the Korteweg-deVries Equation, 10.1002/sapm197757113
2. Baik Jinho, Buckingham Robert, DiFranco Jeffery, Asymptotics of Tracy-Widom Distributions and the Total Integral of a Painlevé II Function, 10.1007/s00220-008-0433-5
3. Baik Jinho, Buckingham Robert, DiFranco Jeffery, Its Alexander, Total integrals of global solutions to Painlevé II, 10.1088/0951-7715/22/5/006
4. Bertola M, On the location of poles for the Ablowitz–Segur family of solutions to the second Painlevé equation, 10.1088/0951-7715/25/4/1179
5. Bohigas O., de Carvalho J. X., Pato M. P., Deformations of the Tracy-Widom distribution, 10.1103/physreve.79.031117
6. Bohigas O., Pato M.P., Missing levels in correlated spectra, 10.1016/j.physletb.2004.05.065
7. Bothner, T.: Transition asymptotics for the painlevé ii transcendent (2015). arXiv:1502.03402 [math-ph]
8. Bothner, T., Deift, P., Its, A., Krasovsky, I.: On the asymptotic behavior of a log gas in the bulk scaling limit in the presence of a varying external potential (2014). arXiv:1407.2910
9. Bothner Thomas, Its Alexander, The nonlinear steepest descent approach to the singular asymptotics of the second Painlevé transcendent, 10.1016/j.physd.2012.02.014
10. Chen Yang, Pruessner Gunnar, Orthogonal polynomials with discontinuous weights, 10.1088/0305-4470/38/12/l01
11. Deift, P.A.: Orthogonal polynomials and random matrices: a Riemann–Hilbert approach. Vol. 3. Courant Lecture Notes in Mathematics. New York University, Courant Institute of Mathematical Sciences, New York. American Mathematical Society, Providence, pp. viii+273 (1999)
12. Deift P., Its A., Krasovsky I., Asymptotics of the Airy-Kernel Determinant, 10.1007/s00220-007-0409-x
13. Deift P., Zhou X., A Steepest Descent Method for Oscillatory Riemann--Hilbert Problems. Asymptotics for the MKdV Equation, 10.2307/2946540
14. Deift P., Kriecherbauer T., McLaughlin K. T‐R, Venakides S., Zhou X., Strong asymptotics of orthogonal polynomials with respect to exponential weights, 10.1002/(sici)1097-0312(199912)52:12<1491::aid-cpa2>3.3.co;2-r
15. 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
16. Deift Percy, Gioev Dimitri, Universality at the edge of the spectrum for unitary, orthogonal, and symplectic ensembles of random matrices, 10.1002/cpa.20164
17. Deift Percy, Its Alexander, Krasovsky Igor, Asymptotics of Toeplitz, Hankel, and Toeplitz+Hankel determinants with Fisher-Hartwig singularities, 10.4007/annals.2011.174.2.12
18. Dyson, F.J.: The Coulomb fluid and the fifth Painlevé transcendent. In: Yang, C.N., Liu, C.S., Yau, S.-T. (eds.) pp. 131–146. International Press, Cambridge (1995)
19. Fokas A. S., Its A. R., Kitaev A. V., The isomonodromy approach to matric models in 2D quantum gravity, 10.1007/bf02096594
20. Fokas Athanassios, Its Alexander, Kapaev Andrei, Novokshenov Victor, Painlevé Transcendents, ISBN:9780821836514, 10.1090/surv/128
21. Its A., Krasovsky I., Hankel determinant and orthogonal polynomials for the Gaussian weight with a jump, 10.1090/conm/458/08938
22. Its A R, Kuijlaars A B J, Östensson J, Asymptotics for a special solution of the thirty fourth Painlevé equation, 10.1088/0951-7715/22/7/002
23. Its Alexander, Discrete Painlevé Equations and Orthogonal Polynomials, Symmetries and Integrability of Difference Equations ISBN:9780511997136 p.139-159, 10.1017/cbo9780511997136.007
24. Its Alexander R., Large N Asymptotics in Random Matrices, Random Matrices, Random Processes and Integrable Systems (2011) ISBN:9781441995131 p.351-413, 10.1007/978-1-4419-9514-8_5
25. Johansson Kurt, On fluctuations of eigenvalues of random Hermitian matrices, 10.1215/s0012-7094-98-09108-6
26. Kapaev Andrei, Global asymptotics of the second Painlevé transcendent, 10.1016/0375-9601(92)90271-m
27. Krasovsky I. V., Correlations of the characteristic polynomials in the Gaussian unitary ensemble or a singular Hankel determinant, 10.1215/s0012-7094-07-13936-x
28. Mehta, M.L.: Random matrices. Third. Vol. 142. Pure and Applied Mathematics (Amsterdam), pp. xviii+688. Elsevier/Academic Press, Amsterdam (2004)
29. Plancherel M., Rotach W., Sur les valeurs asymptotiques des polynomes d'Hermite $$H_n (x) = ( - I)^n e^{\frac{{x^2 }}{2}} \frac{{d^n }}{{dx^n }}\left( {e^{ - \frac{{x^2 }}{2}} } \right),$$, 10.1007/bf01208365
30. Romik D.: The Surprising Mathematics of Longest Increasing Subsequences, Institute of Mathematical Statistics Textbooks. Cambridge University Press, Cambridge (2015)
31. Tracy Craig A., Widom Harold, Level-spacing distributions and the Airy kernel, 10.1007/bf02100489
32. Xu Shuai-Xia, Dai Dan, Zhao Yu-Qiu, Critical Edge Behavior and the Bessel to Airy Transition in the Singularly Perturbed Laguerre Unitary Ensemble, 10.1007/s00220-014-2131-9
33. Xu Shuai-Xia, Zhao Yu-Qiu, Painlevé XXXIV Asymptotics of Orthogonal Polynomials for the Gaussian Weight with a Jump at the Edge : Painlevé XXXIV Asymptotics of Orthogonal Polynomials, 10.1111/j.1467-9590.2010.00512.x