User menu

Accès à distance ? S'identifier sur le proxy UCLouvain

Asymptotics of Hankel Determinants With a One-Cut Regular Potential and Fisher–Hartwig Singularities

  • Open access
  • PDF
  • 540.02 K
  1. Akemann, The Oxford Hand of Random Matrix Theory (2011)
  2. Anderson, G. W. , A.Guionnet, and O.Zeitouni. An Introduction to Random Matrices. Cambridge Studies in Advanced Mathematics, vol. 118. Cambridge: Cambridge University Press, 2010.
  3. Basor Estelle, Asymptotic formulas for Toeplitz determinants, 10.1090/s0002-9947-1978-0493480-x
  4. Basor E., , 10.1512/iumj.1979.28.28070
  5. Berestycki, Random Hermitian Matrices and Gaussian Multiplicative Chaos
  6. Berggren Tomas, Duits Maurice, Mesoscopic Fluctuations for the Thinned Circular Unitary Ensemble, 10.1007/s11040-017-9250-4
  7. M. Bleher Pavel, Its Alexander, Asymptotics of the partition function of a random matrix model, 10.5802/aif.2147
  8. Bohigas O., Pato M.P., Missing levels in correlated spectra, 10.1016/j.physletb.2004.05.065
  9. Bohigas, Phys. Rev. E, 74, no. (2006)
  10. Bothner, Non-oscillatory Asymptotics, 04462 (1702)
  11. Bothner Thomas, Deift Percy, Its Alexander, Krasovsky Igor, On the Asymptotic Behavior of a Log Gas in the Bulk Scaling Limit in the Presence of a Varying External Potential I, 10.1007/s00220-015-2357-1
  12. Bothner, On the Asymptotic Behavior of a Log Gas in the Bulk Scaling Limit in the Presence of a Varying External Potential II, 213 (2017)
  13. Böttcher Albrecht, Silbermann Bernd, Toeplitz Operators and Determinants Generated by Symbols with One Fisher-Hartwig Singularity, 10.1002/mana.19861270108
  14. Charlier Christophe, Claeys Tom, Asymptotics for Toeplitz determinants: Perturbation of symbols with a gap, 10.1063/1.4908105
  15. Charlier Christophe, Claeys Tom, Thinning and conditioning of the circular unitary ensemble, 10.1142/s2010326317500071
  16. Charlier, Asymptotics for Hankel determinants associated to a Hermite weight with a varying discontinuity
  17. Claeys, SIGMA Symmetry Integrability Geom. Methods Appl, 12, 44 (2016)
  18. Claeys T., Grava T., McLaughlin K. D. T.-R., Asymptotics for the Partition Function in Two-Cut Random Matrix Models, 10.1007/s00220-015-2412-y
  19. Claeys T., Krasovsky I., Toeplitz determinants with merging singularities, 10.1215/00127094-3164897
  20. Daley, An Introduction to the Theory of Point Processes: Volume II: General Theory and structure. (2008)
  21. Deaño Alfredo, Simm Nicholas J., On the probability of positive-definiteness in the gGUE via semi-classical Laguerre polynomials, 10.1016/j.jat.2017.04.004
  22. Deift, Amer. Math. Soc, 3 (2000)
  23. 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
  24. Deift, On the Asymptotics of a Toeplitz Determinant With singularities (2014)
  25. Deift P, Kriecherbauer T, McLaughlin K.T.-R, New Results on the Equilibrium Measure for Logarithmic Potentials in the Presence of an External Field, 10.1006/jath.1997.3229
  26. 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
  27. Deift, Comm. Pure Appl. Math, 52, 1491 (1999)
  28. Deift P., Zhou X., A steepest descent method\\ for oscillatory Riemann-Hilbert problems, 10.1090/s0273-0979-1992-00253-7
  29. Deift P., Zhou X., A Steepest Descent Method for Oscillatory Riemann--Hilbert Problems. Asymptotics for the MKdV Equation, 10.2307/2946540
  30. Ehrhardt, Operator Theory: Adv. Appl., 124, 217 (2001)
  31. Ercolani N., McLaughlin K., 10.1155/s1073792803211089
  32. Fisher, Advan. Chem. Phys, 15, 333 (1968)
  33. Fokas A. S., Its A. R., Kitaev A. V., The isomonodromy approach to matric models in 2D quantum gravity, 10.1007/bf02096594
  34. Forrester P. J., Frankel N. E., Applications and generalizations of Fisher–Hartwig asymptotics, 10.1063/1.1699484
  35. Foulquié Moreno A., Martínez-Finkelshtein A., Sousa V.L., On a conjecture of A. Magnus concerning the asymptotic behavior of the recurrence coefficients of the generalized Jacobi polynomials, 10.1016/j.jat.2009.08.006
  36. Gakhov, Boundary Value Problems. Oxford: Pergamon Press, 1966. Reprinted by (1990)
  37. Its A., Krasovsky I., Hankel determinant and orthogonal polynomials for the Gaussian weight with a jump, 10.1090/conm/458/08938
  38. Johansson Kurt, On fluctuations of eigenvalues of random Hermitian matrices, 10.1215/s0012-7094-98-09108-6
  39. Johansson, 1 (2006)
  40. Kallenberg, Inst. Stat. Mimeo Ser. (1974)
  41. Keating J. P., Snaith N. C., Random Matrix Theory and ζ(1/2+ it), 10.1007/s002200000261
  42. 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
  43. Kuijlaars A.B.J., McLaughlin K.T.-R., Van Assche W., Vanlessen M., The Riemann–Hilbert approach to strong asymptotics for orthogonal polynomials on [−1,1], 10.1016/j.aim.2003.08.015
  44. Lambert
  45. Mehta, Random matrices, 3rd ed. Pure and Applied Mathematics Series (2004)
  46. Olver, NIST Handbook of Mathematical Functions. (2010)
  47. Saff Edward B., Totik Vilmos, Logarithmic Potentials with External Fields, ISBN:9783642081736, 10.1007/978-3-662-03329-6
  48. Soshnikov A, Determinantal random point fields, 10.1070/rm2000v055n05abeh000321
  49. Szegő, Orthogonal Polynomials (1959)
  50. Widom Harold, The Strong Szego Limit Theorem for Circular Arcs, 10.1512/iumj.1972.21.21022
  51. Widom Harold, Toeplitz Determinants with Singular Generating Functions, 10.2307/2373789
  52. Wu Xiao-Bo, Xu Shuai-Xia, Zhao Yu-Qiu, Gaussian Unitary Ensemble with Boundary Spectrum Singularity and σ-Form of the Painlevé II Equation : Gaussian Unitary Ensemble with Boundary Spectrum Singularity, 10.1111/sapm.12197
Bibliographic reference Charlier, Christophe. Asymptotics of Hankel Determinants With a One-Cut Regular Potential and Fisher–Hartwig Singularities. In: International Mathematics Research Notices, Vol. rny009, no./, p. / (2018)
Permanent URL http://hdl.handle.net/2078.1/196034