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We investigate the asymptotic behavior of a generalized sine kernel acting on a finite size interval [-q,q].
M. Kac, "Toeplitz matrices, translation kernels and related problem in probability." , Duke Math. J. 21
1954
Earlier work this paper cites.
M. Gaudin and M. L. Mehta, "On the density of eigenvalues of a random matrix." , Nucl. Phys 18
1960
Earlier work this paper cites.
M. Gaudin, "Sur la loi limite de l’espacement des valeurs propres d’une matrice aléatoire." , Nucl. Phys. 25
1961
Earlier work this paper cites.
N. I. Akhiezer, "The continuous analogues of some Theorems on Toeplitz matrices." , Ukrainian Math. J. 16
1964
Earlier work this paper cites.
A. Lenard, Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons , J. Math. Phys. 5
1964
Earlier work this paper cites.
A. Lenard, One-dimensional impenetrable bosons in thermal equilibrium , J. Math. Phys. 7
1966
Earlier work this paper cites.
H. Widom, "The strong Szegö limit theorem for circular arcs." , Indiana Univ. Math. J. 21
1971
Earlier work this paper cites.
J. des Cloizeaux and M. L. Mehta, "Asymptotic behaviour of spacing distributions for the eigenvalues of random matrices." , J. Math. Phys. 14
1973
Earlier work this paper cites.
F. Dyson, "Fredholm determinants and inverse scattering problems." , Comm. Math. Phys. 47
1976
Earlier work this paper cites.
F. D. M. Haldane, "General relation of correlation exponents and spectral properties of one-dimensional Fermi systems: Application to the anisotropic s = 1/2 Heisenberg chain." , Phys. Rev. Lett. 45
1980
Earlier work this paper cites.
M. Jimbo, T. Miwa, Y. Mori, and M. Sato, "Density matrix of an impenetrable Bose gas and the fifth Painlevé transcendent." , Physica D 1
1980
Earlier work this paper cites.
F. D. M. Haldane, "Demonstration of the “Luttinger liquid“ character of Bethe-ansatz soluble models of 1-D quantum fluids" , Phys. Lett. A 81
1981
Earlier work this paper cites.
F. D. M. Haldane, "Luttinger liquid theory of one-dimensional quantum fluids: I. Properties of the Luttinger model and their extension to the general 1D interacting spinless Fermi gas" , J. Phys. C: Solid State Phys. 14
1981
Earlier work this paper cites.
A. R. Its, Asymptotic behaviour of the solutions to the nonlinear Schrödinger equation, and isomonodromic deformations of systems of linear differential equations , Dokl. Akad. Nauk SSSR 261
1981
Earlier work this paper cites.
B. M. McCoy, J. H. H. Perk, and R. E. Shrock, "Time-dependent correlation functions of the transverse Ising chain at the critical magnetic field." , Nucl. Phys. B 220
1983
Cited alongside, same era.
N. M. Bogoliubov, A. G. Izergin, and V. E. Korepin, "Critical exponents for integrable models" , Nucl. Phys. B. 275
1986
Cited alongside, same era.
B. M. McCoy and S. Tang "Connection formulae for Painlevé V functions II. The delta function Bose gas problem." , Physica D 20
1986
Cited alongside, same era.
A.R. Its, A.G. Izergin, and V.E. Korepin, Long-distance asymptotics of temperature correlators of the impenetrable Bose gas , Commun. Math. Phys. 130
1990
Cited alongside, same era.
A.R. Its, A.G. Izergin, and V.E. Korepin, Temperature correlators of the impenetrable Bose gas as an integrable system , Commun. Math. Phys. 129
1990
P. A. Deift and X. Zhou, Long-time behaviour of the non-focusing nonlinear schr odinger equation - a case study , Lectures in Mathematical Sciences, vol. 5, University of Tokyo, Tokyo, 1994
1994
Later among the works it cites.
H. Widom, "The asymptotics of a continuous analogue of orthogonal polynomials." , J. Approx. th. 77
1994
Later among the works it cites.
A. M. Budylin and V. S. Buslaev, "Quasiclassical asymptotics of the resolvent of an integral convolution operator with a sine kernel on a finite interval." , Algebra i Analiz n o no 6 7
1995
Later among the works it cites.
1995
Later among the works it cites.
P. A. Deift, A.R. Its and X. Zhou, "A Riemann–Hilbert approach to asymptotics problems arising in the theory of random matrix models and also in the theory of integrable statistical mechanics." , Ann. Math. 146
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Cited alongside, same era.
A.R. Its, A.G. Izergin, V.E. Korepin, and N.A. Slavonv, "Differential equations for quantum correlation functions." , Int. J. Mod. Physics B4
1990
Cited alongside, same era.
V. E. Korepin and N. A. Slavnov, The time dependent correlation function of an impenetrable Bose gas as a Fredholm minor. I , Comm. Math. Phys. 129
1990
Cited alongside, same era.
A.R. Its, A.G. Izergin, V.E. Korepin, and G. G. Varguzin, Large time and distance asymptotics of the correlator of the impenetrable bosons at finite temperature , Physica D 54
1991
Cited alongside, same era.
E. L. Basor and C. A. Tracy, "Some problems associated with the asymptotics of τ \tau functions." , Suaikaguku n o no 3 30
1992
Cited alongside, same era.
F. Colomo, A. G. Izergin, V. E. Korepin, and V. Tognetti, Correlators in the Heisenberg XX0 chain as Fredholm determinants , Phys. Lett. A 169
1992
Cited alongside, same era.
N. M. Bogoliubov, A. G. Izergin, and V. E. Korepin, "Quantum Inverse Scattering Method, Correlation Functions and Algebraic Bethe Ansatz." , Cambridge monograph on mathematical physics., 1993
1993
Cited alongside, same era.
F. Colomo, A. G. Izergin, V. E. Korepin, and V. Tognetti, Temperature correlation functions in the XX0 Heisenberg chain , Teor. Mat. Fiz. 94
1993
Cited alongside, same era.
1997
Later among the works it cites.
P. A. Deift and X. Zhou, "A steepest descent method for oscillatory Riemann–Hilbert problems." , Intl. Math. Res. 6
1997
Later among the works it cites.
V.V. Cheianov and M.R. Zvonarev, "Zero temperature correlation functions for the impenetrable fermion gas." , J. Phys. A:Math. Gen., 37
2004
Later among the works it cites.
V. I. Krasovsky, "Gap probability in the spectrum of random matrices and asymptotics of polynomials orthogonal on an arc of the unit circle." , Int. Math. Res. Not. 2004
2004
Later among the works it cites.
A.B.J. Kuijlaars, K.T.-R. McLaughlin, W. Van Assche, and M. Vanlessen, "The Riemann–Hilbert approach to strong asymptotics for orthogonal polynomials on [-1,1]." , Advances in Math. 188
2004
Later among the works it cites.
T. Ehrhardt, "dyson’s constant in the asymptotics of the fredholm determinant of the sine kernel." , Comm. Math. Phys. 262
2006
Later among the works it cites.
P. A. Deift, A. R. Its, I. Krasovsky and X. Zhou, The Widom-Dyson constant for the gap probability in random matrix theory , J. Comput. Appl. Math. 202 (2007), no. 1, 26–47
2007
Later among the works it cites.
A. R. Its, I. Krasovsky, Hankel determinant and orthogonal polynomials for the Gaussian weight with a jump , Contemporary Mathematics (AMS series) 458
2008
Closest in time.
N. Kitanine, K. K. Kozlowski, J.-M. Maillet, N.A. Slavnov, and V. Terras, "Algebraic Bethe ansatz approach to the asymptotic behavior of correlation functions." , J. Stat. Mech. (2009) P04003
2009
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