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We show that the ratio of a discrete Toeplitz/Hankel determinant and its continuous counterpart equals a Freholm determinant involving continuous orthogonal polynomials.
Orthogonal Polynomials
G. Szegö · 1939
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Coincidence probabilities
S. Karlin and J. McGregor · 1959
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Convergence of Probability Measures
P. Billingsley · 1968
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The isomonodromy approach to matrix models in 2 2 D quantum gravity
A. S. Fokas, A. R. Its, and A. V. Kitaev · 1992
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A steepest descent method for oscillatory Riemann-Hilbert problems. Asymptotics for the MKdV equation
P. Deift and X. Zhou · 1993
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Level-spacing distributions and the Airy kernel
C. A. Tracy and H. Widom · 1994
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Non-colliding Brownian motions on the circle
D. G. Hobson and W. Werner · 1996
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The shape of a typical boxed plane partition
H. Cohn, M. Larsen, and J. Propp · 1998
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On the distribution of the length of the longest increasing subsequence of random permutations
J. Baik, P. Deift, and K. Johansson · 1999
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Orthogonal polynomials and random matrices: a Riemann-Hilbert approach
P. Deift · 1999
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Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory
P. Deift, T. Kriecherbauer, K. T.-R. McLaughlin, S. Venakides, and X. Zhou · 1999
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J. Baik · 2000
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K. Johansson · 2000
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Optimal tail estimates for directed last passage site percolation with geometric random variables
J. Baik, P. Deift, K. T.-R. McLaughlin, P. D. Miller, and X. Zhou · 2001
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Random walks and random permutations
P. J. Forrester · 2001
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K. Johansson · 2002
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Scale invariance of the PNG droplet and the Airy process
M. Prähofer and H. Spohn · 2002
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Nonintersecting Brownian excursions
C. A. Tracy and H. Widom · 2007
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Asymptotics of Tracy-Widom distributions and the total integral of a Painlevé II function
J. Baik, R. Buckingham, and J. DiFranco · 2008
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Asymptotics of the Airy-kernel determinant
P. Deift, A. R. Its, and I. Krasovsky · 2008
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Maximum distributions of bridges of noncolliding Brownian paths
N. Kobayashi, M. Izumi, and M. Katori · 2008
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Exact distribution of the maximal height of p vicious walkers
G. Schehr, S. N. Majumdar, A. Comtet, and J. Random-Furling · 2008
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Dyson’s nonintersecting Brownian motions with a few outliers
M. Adler, J. Delépine, and P. van Moerbeke · 2009
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K. Johansson · 2003
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Szegő orthogonal polynomials with respect to an analytic weight: canonical representation and strong asymptotics
A. Martínez-Finkelshtein, K. T.-R. McLaughlin, and E. B. Saff · 2006
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Discrete orthogonal polynomials. Asymptotics and applications
J. Baik, T. Kriecherbauer, K. T.-R. McLaughlin, and P. D. Miller · 2007
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W. Y. C. Chen, E. Y. P. Deng, R. R. X. Du, R. P. Stanley, and C. H. Yan · 2007
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Non-intersecting random walks in the neighborhood of a symmetric tacnode
M. Adler, P. Ferrari, and P. van Moerbeke
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Note sur une relation les integrales definies des produits des fonctions
C. Andréief
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Shuffling algorithm for boxed plane partitions
A. Borodin and V. Gorin · 2009
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Asymptotics in ASEP with step initial condition
C. A. Tracy and H. Widom · 2009
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Non-intersecting Brownian walkers and Yang-Mills theory on the sphere
P. J. Forrester, S. N. Majumdar, and G. Schehr · 2011
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Nonintersecting Brownian motions on the half-line and discrete Gaussian orthogonal polynomials
K. Liechty · 2012
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