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Volumn , Issue 164, 2007, Pages 1-171

Discrete orthogonal polynomials: Asymptotics and applications

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EID: 33847198993     PISSN: 00662313     EISSN: None     Source Type: Book Series    
DOI: None     Document Type: Article
Times cited : (103)

References (56)
  • 2
    • 0035824491 scopus 로고    scopus 로고
    • Asymptotics of discrete orthogonal polynomials and the continuum limit of the Toda lattice
    • A. Aptekarev and W. Van Assche, "Asymptotics of discrete orthogonal polynomials and the continuum limit of the Toda lattice," J. Phys. A: Math Gen., 34, 10627-10637, 2001.
    • (2001) J. Phys. A: Math Gen , vol.34 , pp. 10627-10637
    • Aptekarev, A.1    Van Assche, W.2
  • 3
    • 33847187518 scopus 로고    scopus 로고
    • Riemann-Hilbert problems and random permutations,
    • Ph.D Thesis, Courant Institute of Mathematical Sciences, New York University
    • J. Baik, "Riemann-Hilbert problems and random permutations," Ph.D Thesis, Courant Institute of Mathematical Sciences, New York University, 1999.
    • (1999)
    • Baik, J.1
  • 4
    • 0033443150 scopus 로고    scopus 로고
    • On the distribution of the length of the longest increasing subsequence of random permutations
    • J. Baik, P. Deift, and K. Johansson, "On the distribution of the length of the longest increasing subsequence of random permutations," J. Amer. Math. Soc., 12, 1119-1178, 1999.
    • (1999) J. Amer. Math. Soc , vol.12 , pp. 1119-1178
    • Baik, J.1    Deift, P.2    Johansson, K.3
  • 5
    • 0038578323 scopus 로고    scopus 로고
    • Uniform asymptotics for polynomials orthogonal with respect to a general class of discrete weights and universality results for associated ensembles: Announcement of results
    • J. Baik, T. Kriecherbauer, K. D. T.-R. McLaughlin, and P. D. Miller, "Uniform asymptotics for polynomials orthogonal with respect to a general class of discrete weights and universality results for associated ensembles: announcement of results," Int. Math. Res. Not., 15, 821-858, 2003.
    • (2003) Int. Math. Res. Not , vol.15 , pp. 821-858
    • Baik, J.1    Kriecherbauer, T.2    McLaughlin, K.D.T.-R.3    Miller, P.D.4
  • 6
    • 0033244830 scopus 로고    scopus 로고
    • Semiclassical asymptotics of orthogonal polynomials, Riemann-Hilbert problem, and universality in the matrix model
    • P. Bleher and A. Its, "Semiclassical asymptotics of orthogonal polynomials, Riemann-Hilbert problem, and universality in the matrix model," Ann. of Math., 150, 185-266, 1999.
    • (1999) Ann. of Math , vol.150 , pp. 185-266
    • Bleher, P.1    Its, A.2
  • 7
    • 0037445183 scopus 로고    scopus 로고
    • Dispersionless Toda and Toeplitz operators
    • A. Bloch, F. Golse, T. Paul, and A. Uribe, "Dispersionless Toda and Toeplitz operators," Duke Math. J., 117, 157-196, 2003.
    • (2003) Duke Math. J , vol.117 , pp. 157-196
    • Bloch, A.1    Golse, F.2    Paul, T.3    Uribe, A.4
  • 8
    • 0346737796 scopus 로고    scopus 로고
    • Riemann-Hilbert problem and the discrete Bessel kernel
    • A. Borodin, "Riemann-Hilbert problem and the discrete Bessel kernel," Int. Math. Res. Not., 9, 467-494, 2000.
    • (2000) Int. Math. Res. Not , vol.9 , pp. 467-494
    • Borodin, A.1
  • 9
    • 0036390386 scopus 로고    scopus 로고
    • Duality of orthogonal polynomials on a finite set
    • A. Borodin, "Duality of orthogonal polynomials on a finite set," J. Statist. Phys., 109, 1109-1120, 2002.
    • (2002) J. Statist. Phys , vol.109 , pp. 1109-1120
    • Borodin, A.1
  • 10
    • 0038209546 scopus 로고    scopus 로고
    • Discrete gap probabilities and discrete Painlevé equations
    • A. Borodin, "Discrete gap probabilities and discrete Painlevé equations," Duke Math. J., 117, 489-542, 2003.
    • (2003) Duke Math. J , vol.117 , pp. 489-542
    • Borodin, A.1
  • 11
    • 0037343481 scopus 로고    scopus 로고
    • Distribution of the first particle in discrete orthogonal polynomial ensembles
    • A. Borodin and D. Boyarchenko, "Distribution of the first particle in discrete orthogonal polynomial ensembles," Comm. Math. Phys., 234, 287-338, 2003.
    • (2003) Comm. Math. Phys , vol.234 , pp. 287-338
    • Borodin, A.1    Boyarchenko, D.2
  • 12
    • 33847175324 scopus 로고    scopus 로고
    • A. Borodin and G. Olshanski, z-measures on partitions, Robinson-Schensted-Knuth correspondence, and β = 2 random matrix ensembles, in Random Matrix Models and Their Applications, Math. Sci. Res. Inst. Publ., 40, 71-94, Cambridge Univ. Press, Cambridge, 2001.
    • A. Borodin and G. Olshanski, "z-measures on partitions, Robinson-Schensted-Knuth correspondence, and β = 2 random matrix ensembles," in Random Matrix Models and Their Applications, Math. Sci. Res. Inst. Publ., 40, 71-94, Cambridge Univ. Press, Cambridge, 2001.
  • 13
    • 21644449975 scopus 로고    scopus 로고
    • Harmonic analysis on the infinite-dimensional unitary group and determinantal point processes
    • A. Borodin and G. Olshanski, "Harmonic analysis on the infinite-dimensional unitary group and determinantal point processes," Ann. of Math., 161, 1319-1422, 2005.
    • (2005) Ann. of Math , vol.161 , pp. 1319-1422
    • Borodin, A.1    Olshanski, G.2
  • 14
    • 0034390399 scopus 로고    scopus 로고
    • Asymptotics of Plancherel measures for symmetric groups
    • A. Borodin, A. Okounkov, and G. Olshanski, "Asymptotics of Plancherel measures for symmetric groups," J. Amer. Math. Soc., 13, 481-515, 2000.
    • (2000) J. Amer. Math. Soc , vol.13 , pp. 481-515
    • Borodin, A.1    Okounkov, A.2    Olshanski, G.3
  • 15
    • 0001580766 scopus 로고    scopus 로고
    • The shape of a typical boxed plane partition
    • H. Cohn, M. Larsen, and J. Propp, "The shape of a typical boxed plane partition," New York J. Math., 4, 137-165, 1998.
    • (1998) New York J. Math , vol.4 , pp. 137-165
    • Cohn, H.1    Larsen, M.2    Propp, J.3
  • 18
    • 0003346458 scopus 로고    scopus 로고
    • Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach
    • Courant Institute of Mathematical Sciences, New York
    • P. Deift, Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach, Courant Lecture Notes in Mathematics, 3, Courant Institute of Mathematical Sciences, New York, 1999.
    • (1999) Courant Lecture Notes in Mathematics , vol.3
    • Deift, P.1
  • 20
    • 0000743268 scopus 로고    scopus 로고
    • New results on the equilibrium measure for logarithmic potentials in the presence of an external field
    • P. Deift, T. Kriecherbauer, and K. T.-R. McLaughlin, "New results on the equilibrium measure for logarithmic potentials in the presence of an external field," J. Approx. Theory, 95, 388-475, 1998.
    • (1998) J. Approx. Theory , vol.95 , pp. 388-475
    • Deift, P.1    Kriecherbauer, T.2    McLaughlin, K.T.-R.3
  • 22
    • 0033440723 scopus 로고    scopus 로고
    • 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, "Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory," Comm. Pure Appl. Math., 52, 1335-1425, 1999.
    • (1999) Comm. Pure Appl. Math , vol.52 , pp. 1335-1425
    • Deift, P.1    Kriecherbauer, T.2    McLaughlin, K.T.-R.3    Venakides, S.4    Zhou, X.5
  • 24
    • 1842665167 scopus 로고    scopus 로고
    • New results in small dispersion KdV by an extension of the steepest-descent method for Riemann-Hilbert problems
    • P. Deift, S. Venakides, and X. Zhou, "New results in small dispersion KdV by an extension of the steepest-descent method for Riemann-Hilbert problems," Int. Math. Res. Not., 6, 286-299, 1997.
    • (1997) Int. Math. Res. Not , vol.6 , pp. 286-299
    • Deift, P.1    Venakides, S.2    Zhou, X.3
  • 25
    • 0001525213 scopus 로고
    • A steepest-descent method for oscillatory Riemann-Hilbert problems: Asymptotics for the mKdV equation
    • P. Deift and X. Zhou, "A steepest-descent method for oscillatory Riemann-Hilbert problems: asymptotics for the mKdV equation," Ann. of Math., 137, 295-368, 1993.
    • (1993) Ann. of Math , vol.137 , pp. 295-368
    • Deift, P.1    Zhou, X.2
  • 26
    • 84990647031 scopus 로고
    • Asymptotics for the Painlevé II equation
    • P. Deift and X. Zhou, "Asymptotics for the Painlevé II equation," Comm. Pure Appl. Math., 48, 277-337, 1995.
    • (1995) Comm. Pure Appl. Math , vol.48 , pp. 277-337
    • Deift, P.1    Zhou, X.2
  • 27
    • 0000614428 scopus 로고    scopus 로고
    • Constrained energy problems with applications to orthogonal polynomials of a discrete variable
    • P. D. Dragnev and E. B. Saff, "Constrained energy problems with applications to orthogonal polynomials of a discrete variable," J. d'Analyse Math., 72, 223-259, 1997.
    • (1997) J. d'Analyse Math , vol.72 , pp. 223-259
    • Dragnev, P.D.1    Saff, E.B.2
  • 28
    • 0001282264 scopus 로고    scopus 로고
    • A problem in potential theory and zero asymptotics of Krawtchouk polynomials
    • P. D. Dragnev and E. B. Saff, "A problem in potential theory and zero asymptotics of Krawtchouk polynomials," J. Approx. Theory, 102, 120-140, 2000.
    • (2000) J. Approx. Theory , vol.102 , pp. 120-140
    • Dragnev, P.D.1    Saff, E.B.2
  • 29
    • 0345862213 scopus 로고    scopus 로고
    • Step fluctuations for a faceted crystal
    • P. Ferrari and H. Spohn, "Step fluctuations for a faceted crystal," J. Statist. Phys., 113, 1-46, 2003.
    • (2003) J. Statist. Phys , vol.113 , pp. 1-46
    • Ferrari, P.1    Spohn, H.2
  • 30
    • 0000533283 scopus 로고
    • Discrete Painlevé equations and their appearance in quantum gravity
    • A. S. Fokas, A. R. Its, and A. V. Kitaev, "Discrete Painlevé equations and their appearance in quantum gravity," Comm. Math. Phys., 142, 313-344, 1991.
    • (1991) Comm. Math. Phys , vol.142 , pp. 313-344
    • Fokas, A.S.1    Its, A.R.2    Kitaev, A.V.3
  • 31
    • 0032294916 scopus 로고    scopus 로고
    • Strong asymptotics for Krawtchouk polynomials
    • M. E. H. Ismail and P. Simeonov, "Strong asymptotics for Krawtchouk polynomials," J. Comput. Appl. Math., 100, 121-144, 1998.
    • (1998) J. Comput. Appl. Math , vol.100 , pp. 121-144
    • Ismail, M.E.H.1    Simeonov, P.2
  • 32
    • 0034340689 scopus 로고    scopus 로고
    • Shape fluctuations and random matrices
    • K. Johansson, "Shape fluctuations and random matrices," Comm. Math. Phys., 209, 437-476, 2000.
    • (2000) Comm. Math. Phys , vol.209 , pp. 437-476
    • Johansson, K.1
  • 33
    • 0035626398 scopus 로고    scopus 로고
    • Discrete orthogonal polynomial ensembles and the Plancherel measure
    • K. Johansson, "Discrete orthogonal polynomial ensembles and the Plancherel measure," Ann. of Math., 153, 259-296, 2001.
    • (2001) Ann. of Math , vol.153 , pp. 259-296
    • Johansson, K.1
  • 34
    • 0036628218 scopus 로고    scopus 로고
    • Non-intersecting paths, random tilings and random matrices
    • K. Johansson, "Non-intersecting paths, random tilings and random matrices," Probab. Theory Related Fields, 123, 225-280, 2002.
    • (2002) Probab. Theory Related Fields , vol.123 , pp. 225-280
    • Johansson, K.1
  • 35
    • 85009055469 scopus 로고    scopus 로고
    • Semiclassical Soliton Ensembles for the Focusing Nonlinear Schrödinger Equation
    • Princeton University Press, Princeton
    • S. Kamvissis, K. T.-R. McLaughlin, and P. D. Miller, Semiclassical Soliton Ensembles for the Focusing Nonlinear Schrödinger Equation, Annals of Mathematics Studies series, volume 154, Princeton University Press, Princeton, 2003.
    • (2003) Annals of Mathematics Studies series , vol.154
    • Kamvissis, S.1    McLaughlin, K.T.-R.2    Miller, P.D.3
  • 36
    • 0034664307 scopus 로고    scopus 로고
    • On the finite-gap ansatz in the continuum limit of the Toda lattice
    • A. B. J. Kuijlaars, "On the finite-gap ansatz in the continuum limit of the Toda lattice," Duke Math. J., 104, 433-462, 2000.
    • (2000) Duke Math. J , vol.104 , pp. 433-462
    • Kuijlaars, A.B.J.1
  • 37
    • 0034398875 scopus 로고    scopus 로고
    • Generic behavior of the density of states in random matrix theory and equilibrium problems in the presence of real analytic external fields
    • A. B. J. Kuijlaars and K. T.-R. McLaughlin, "Generic behavior of the density of states in random matrix theory and equilibrium problems in the presence of real analytic external fields," Comm. Pure Appl. Math., 53, 736-785, 2000.
    • (2000) Comm. Pure Appl. Math , vol.53 , pp. 736-785
    • Kuijlaars, A.B.J.1    McLaughlin, K.T.-R.2
  • 39
    • 0032207940 scopus 로고    scopus 로고
    • Zero distributions for discrete orthogonal polynomials
    • A. B. J. Kuijlaars and E. A. Rakhmanov, "Zero distributions for discrete orthogonal polynomials," J. Comput. Appl. Math., 99, 255-274, 1998.
    • (1998) J. Comput. Appl. Math , vol.99 , pp. 255-274
    • Kuijlaars, A.B.J.1    Rakhmanov, E.A.2
  • 40
    • 0001114597 scopus 로고    scopus 로고
    • The asymptotic zero distribution of orthogonal polynomials with varying recurrence coefficients
    • A. B. J. Kuijlaars and W. Van Assche, "The asymptotic zero distribution of orthogonal polynomials with varying recurrence coefficients," J. Approx. Theory, 99, 167-197, 1999.
    • (1999) J. Approx. Theory , vol.99 , pp. 167-197
    • Kuijlaars, A.B.J.1    Van Assche, W.2
  • 42
    • 0004163930 scopus 로고
    • Second edition, Academic Press, Boston
    • M. L. Mehta, Random Matrices, Second edition, Academic Press, Boston, 1991.
    • (1991) Random Matrices
    • Mehta, M.L.1
  • 43
    • 0036335780 scopus 로고    scopus 로고
    • Asymptotics of semiclassical soliton ensembles: Rigorous justification of the WKB approximation
    • P. D. Miller, "Asymptotics of semiclassical soliton ensembles: rigorous justification of the WKB approximation," Int. Math. Res. Not., 8, 383-454, 2002.
    • (2002) Int. Math. Res. Not , vol.8 , pp. 383-454
    • Miller, P.D.1
  • 44
    • 0000216497 scopus 로고    scopus 로고
    • Modal expansions and completeness relations for some time-dependent Schrödinger equations
    • P. D. Miller and N. N. Akhmediev, "Modal expansions and completeness relations for some time-dependent Schrödinger equations," Physica D, 123, 513-524, 1998.
    • (1998) Physica D , vol.123 , pp. 513-524
    • Miller, P.D.1    Akhmediev, N.N.2
  • 45
    • 0036045704 scopus 로고    scopus 로고
    • An exactly solvable model for the interaction of linear waves with Korteweg-de Vries solitons
    • P. D. Miller and S. R. Clarke, "An exactly solvable model for the interaction of linear waves with Korteweg-de Vries solitons," SIAM J. Math. Anal., 33, 261-285, 2001.
    • (2001) SIAM J. Math. Anal , vol.33 , pp. 261-285
    • Miller, P.D.1    Clarke, S.R.2
  • 47
    • 0003377901 scopus 로고    scopus 로고
    • Infinite wedge and random partitions
    • A. Okounkov, "Infinite wedge and random partitions," Selecta Math. (N.S.), 7, 57-81, 2001.
    • (2001) Selecta Math. (N.S.) , vol.7 , pp. 57-81
    • Okounkov, A.1
  • 48
    • 0038806289 scopus 로고    scopus 로고
    • Correlation function of a Schur process with application to local geometry of a random 3-dimensional Young diagram
    • A. Okounkov and N. Reshetikhin, "Correlation function of a Schur process with application to local geometry of a random 3-dimensional Young diagram," J. Amer. Math. Soc., 16, 581-603, 2003.
    • (2003) J. Amer. Math. Soc , vol.16 , pp. 581-603
    • Okounkov, A.1    Reshetikhin, N.2
  • 49
    • 0001043547 scopus 로고    scopus 로고
    • Equilibrium measure and the distribution of zeros of the extremal polynomials of a discrete variable
    • in Russian
    • E. A. Rakhmanov, "Equilibrium measure and the distribution of zeros of the extremal polynomials of a discrete variable," Mat. Sb., 187, 109-124, 1996 (in Russian).
    • (1996) Mat. Sb , vol.187 , pp. 109-124
    • Rakhmanov, E.A.1
  • 50
    • 0030305556 scopus 로고    scopus 로고
    • English translation
    • English translation: Sbornik:Mathematics, 187, 1213-1228, 1996.
    • (1996) Sbornik:Mathematics , vol.187 , pp. 1213-1228
  • 53
    • 0004073954 scopus 로고
    • Orthogonal Polynomials
    • American Mathematical Society, Providence
    • G. Szego, Orthogonal Polynomials, Colloquium Publications volume 23, American Mathematical Society, Providence, 1991.
    • (1991) Colloquium Publications , vol.23
    • Szego, G.1
  • 54
    • 27644532196 scopus 로고
    • Level-Spacing distributions and the Airy kernel
    • C. Tracy and H. Widom, "Level-Spacing distributions and the Airy kernel," Comm. Math. Phys., 159, 151-174, 1994.
    • (1994) Comm. Math. Phys , vol.159 , pp. 151-174
    • Tracy, C.1    Widom, H.2
  • 55
    • 0032163852 scopus 로고    scopus 로고
    • Correlation functions, cluster functions, and spacing distributions for random matrices
    • C. Tracy and H. Widom, "Correlation functions, cluster functions, and spacing distributions for random matrices," J. Statist. Phys., 92, 809-835, 1998.
    • (1998) J. Statist. Phys , vol.92 , pp. 809-835
    • Tracy, C.1    Widom, H.2
  • 56
    • 0000509583 scopus 로고
    • The Riemann-Hilbert problem and inverse scattering
    • X. Zhou, "The Riemann-Hilbert problem and inverse scattering," SIAM J. Math. Anal., 20, 966-986, 1989.
    • (1989) SIAM J. Math. Anal , vol.20 , pp. 966-986
    • Zhou, X.1


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