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Volumn 55, Issue 6, 2002, Pages 679-727

Application of the τ-Function Theory of Painlevé Equations to Random Matrices: Pv, PIII, the LUE, JUE, and CUE

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EID: 0036254223     PISSN: 00103640     EISSN: None     Source Type: Journal    
DOI: 10.1002/cpa.3021     Document Type: Article
Times cited : (121)

References (42)
  • 1
    • 0001769490 scopus 로고
    • Random matrices, vertex operators and the Virasoro algebra
    • Adler, M.; Shiota, T.; van Moerbeke, P. Random matrices, vertex operators and the Virasoro algebra. Phys. Lett. A 208 (1995), no. 1-2, 67-78.
    • (1995) Phys. Lett. A , vol.208 , Issue.1-2 , pp. 67-78
    • Adler, M.1    Shiota, T.2    Van Moerbeke, P.3
  • 2
    • 0035578398 scopus 로고    scopus 로고
    • Integrals over classical groups, random permutations, Toda and Toeplitz lattices
    • Adler, M.; van Moerbeke, P. Integrals over classical groups, random permutations, Toda and Toeplitz lattices. Comm. Pure Appl. Math. 54 (2001), no. 2, 153-205.
    • (2001) Comm. Pure Appl. Math. , vol.54 , Issue.2 , pp. 153-205
    • Adler, M.1    Van Moerbeke, P.2
  • 3
    • 0001036826 scopus 로고
    • Nonlinear chains and Painlevé equations
    • Adler, V. È. Nonlinear chains and Painlevé equations. Phys. D 73 (1994), no. 4, 335-351.
    • (1994) Phys. D , vol.73 , Issue.4 , pp. 335-351
    • Adler, V.È.1
  • 4
    • 0010151103 scopus 로고    scopus 로고
    • The asymptotics of monotone subsequences of involutions
    • Baik, J.; Rains, E. M. The asymptotics of monotone subsequences of involutions. Duke Math. J. 109 (2001), no. 2, 205-281.
    • (2001) Duke Math. J. , vol.109 , Issue.2 , pp. 205-281
    • Baik, J.1    Rains, E.M.2
  • 5
    • 0035920045 scopus 로고    scopus 로고
    • Random walks and random fixed-point free involutions
    • Baker, T. H.; Forrester, P. J. Random walks and random fixed-point free involutions. J. Phys. A 34 (2001), no. 28, L381-L390.
    • (2001) J. Phys. A , vol.34 , Issue.28
    • Baker, T.H.1    Forrester, P.J.2
  • 6
    • 0032563047 scopus 로고    scopus 로고
    • Random matrix ensembles with an effective extensive external charge
    • Baker, T. H.; Forrester, P. J.; Pearce, P. A. Random matrix ensembles with an effective extensive external charge. J. Phys. A 31 (1998), no. 29, 6087-6101.
    • (1998) J. Phys. A , vol.31 , Issue.29 , pp. 6087-6101
    • Baker, T.H.1    Forrester, P.J.2    Pearce, P.A.3
  • 8
    • 0039016041 scopus 로고    scopus 로고
    • Chazy classes IX-XI of third-order differential equations
    • Cosgrove, C. M. Chazy classes IX-XI of third-order differential equations. Stud. Appl. Math. 104 (2000), no. 3, 171-228.
    • (2000) Stud. Appl. Math. , vol.104 , Issue.3 , pp. 171-228
    • Cosgrove, C.M.1
  • 9
    • 0002865557 scopus 로고
    • Painlevé classification of a class of differential equations of the second order and second degree
    • Cosgrove, C. M.; Scoufis, G. Painlevé classification of a class of differential equations of the second order and second degree. Stud. Appl. Math. 88 (1993), no. 1, 25-87.
    • (1993) Stud. Appl. Math. , vol.88 , Issue.1 , pp. 25-87
    • Cosgrove, C.M.1    Scoufis, G.2
  • 10
    • 0000609652 scopus 로고
    • The spectrum edge of random matrix ensembles
    • Forrester, P. J. The spectrum edge of random matrix ensembles. Nuclear Phys. B 402 (1993), no. 3, 709-728.
    • (1993) Nuclear Phys. B , vol.402 , Issue.3 , pp. 709-728
    • Forrester, P.J.1
  • 11
    • 36449000028 scopus 로고
    • Exact results and universal asymptotics in the Laguerre random matrix ensemble
    • Forrester, P. J. Exact results and universal asymptotics in the Laguerre random matrix ensemble. J. Math. Phys. 35 (1994), no. 5, 2539-2551.
    • (1994) J. Math. Phys. , vol.35 , Issue.5 , pp. 2539-2551
    • Forrester, P.J.1
  • 12
    • 0040776443 scopus 로고
    • Normalization of the wavefunction for the Calogero-Sutherland model with internal degrees of freedom
    • Forrester, P. J. Normalization of the wavefunction for the Calogero-Sutherland model with internal degrees of freedom. Internat. J. Modern Phys. B 9 (1995), no. 10, 1243-1261.
    • (1995) Internat. J. Modern Phys. B , vol.9 , Issue.10 , pp. 1243-1261
    • Forrester, P.J.1
  • 16
    • 21844481595 scopus 로고
    • Complex Wishart matrices and conductance in mesoscopic systems: Exact results
    • Forrester, P. J.; Hughes, T. D. Complex Wishart matrices and conductance in mesoscopic systems: exact results. J. Math. Phys. 35 (1994), no. 12, 6736-6747.
    • (1994) J. Math. Phys. , vol.35 , Issue.12 , pp. 6736-6747
    • Forrester, P.J.1    Hughes, T.D.2
  • 17
    • 0002182643 scopus 로고    scopus 로고
    • Exact Wigner surmise type evaluation of the spacing distribution in the bulk of the scaled random matrix ensembles
    • Forrester, P. J.; Witte, N. S. Exact Wigner surmise type evaluation of the spacing distribution in the bulk of the scaled random matrix ensembles. Lett. Math. Phys. 53 (2000), no. 3, 195-200.
    • (2000) Lett. Math. Phys. , vol.53 , Issue.3 , pp. 195-200
    • Forrester, P.J.1    Witte, N.S.2
  • 18
    • 0035534941 scopus 로고    scopus 로고
    • Application of the τ-function theory of Painlevé equations to random matrices: PIV, PII and the GUE
    • Forrester, P. J.; Witte, N. D. Application of the τ-function theory of Painlevé equations to random matrices: PIV, PII and the GUE. Comm. Math. Phys. 219 (2001), no. 2, 357-398.
    • (2001) Comm. Math. Phys. , vol.219 , Issue.2 , pp. 357-398
    • Forrester, P.J.1    Witte, N.D.2
  • 20
    • 0033239781 scopus 로고    scopus 로고
    • The Jacobi polynomial ensemble and the Painlevé VI equation
    • Haine, L.; Semengue, J.-P. The Jacobi polynomial ensemble and the Painlevé VI equation. J. Math. Phys. 40 (1999), no. 4, 2117-2134.
    • (1999) J. Math. Phys. , vol.40 , Issue.4 , pp. 2117-2134
    • Haine, L.1    Semengue, J.-P.2
  • 21
    • 49049148970 scopus 로고
    • Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. II
    • Jimbo, M.; Miwa, T. Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. II. Phys. D 2 (1981), no. 3, 407-448.
    • (1981) Phys. D , vol.2 , Issue.3 , pp. 407-448
    • Jimbo, M.1    Miwa, T.2
  • 22
    • 2342488264 scopus 로고
    • Density matrix of an impenetrable Bose gas and the fifth Painlevé transcendent
    • Jimbo, M.; Miwa, T.; Môri, Y.; Sato, M. Density matrix of an impenetrable Bose gas and the fifth Painlevé transcendent. Phys. D1 (1980), no. 1, 80-158.
    • (1980) Phys. D , vol.1 , Issue.1 , pp. 80-158
    • Jimbo, M.1    Miwa, T.2    Môri, Y.3    Sato, M.4
  • 23
    • 0034340689 scopus 로고    scopus 로고
    • Shape fluctuations and random matrices
    • Johansson, K. Shape fluctuations and random matrices. Comm. Math. Phys. 209 (2000), no. 2, 437-476.
    • (2000) Comm. Math. Phys. , vol.209 , Issue.2 , pp. 437-476
    • Johansson, K.1
  • 24
    • 0035641726 scopus 로고    scopus 로고
    • On the distribution of the largest eigenvalue in principal components analysis
    • Johnstone, I. M. On the distribution of the largest eigenvalue in principal components analysis. Ann. Statist. 29 (2001), no. 2, 295-327.
    • (2001) Ann. Statist. , vol.29 , Issue.2 , pp. 295-327
    • Johnstone, I.M.1
  • 25
    • 0038498600 scopus 로고    scopus 로고
    • Determinant formulas for the Toda and discrete Toda equations
    • Kajiwara, K.; Masuda, T.; Noumi, M.; Ohta, Y.; Yamada, Y. Determinant formulas for the Toda and discrete Toda equations. Funkcial. Ekvac. 44 (2001), no. 2, 291-307.
    • (2001) Funkcial. Ekvac. , vol.44 , Issue.2 , pp. 291-307
    • Kajiwara, K.1    Masuda, T.2    Noumi, M.3    Ohta, Y.4    Yamada, Y.5
  • 28
    • 0002515824 scopus 로고    scopus 로고
    • Symmetries in the fourth Painlevé equation and Okamoto polynomials
    • Noumi, M.; Yamada, Y. Symmetries in the fourth Painlevé equation and Okamoto polynomials. Nagoya Math. J. 153 (1999), 53-86.
    • (1999) Nagoya Math. J. , vol.153 , pp. 53-86
    • Noumi, M.1    Yamada, Y.2
  • 29
    • 0007117198 scopus 로고
    • IV
    • IV. Math. Ann. 275 (1986), no. 2, 221-255.
    • (1986) Math. Ann. , vol.275 , Issue.2 , pp. 221-255
    • Okamoto, K.1
  • 32
    • 10044262136 scopus 로고    scopus 로고
    • Increasing subsequences and the classical groups
    • Research Paper 12
    • Rains, E. M. Increasing subsequences and the classical groups. Electron. J. Combin. 5 (1998), no. 1, Research Paper 12.
    • (1998) Electron. J. Combin. , vol.5 , Issue.1
    • Rains, E.M.1
  • 33
    • 0034723122 scopus 로고    scopus 로고
    • On a transcendental equation related to Painlevé III, and its discrete forms
    • Ramani, A.; Grammaticos, B.; Tamizhmani, T.; Tamizhmani, K. M. On a transcendental equation related to Painlevé III, and its discrete forms. J. Phys. A 33 (2000), no. 3, 579-590.
    • (2000) J. Phys. A , vol.33 , Issue.3 , pp. 579-590
    • Ramani, A.1    Grammaticos, B.2    Tamizhmani, T.3    Tamizhmani, K.M.4
  • 34
    • 0034215344 scopus 로고    scopus 로고
    • Discrete integrable systems from continuous Painlevé equations through limiting procedures
    • Ramani, A.; Ohta, Y.; Grammaticos, B. Discrete integrable systems from continuous Painlevé equations through limiting procedures. Nonlinearity 13 (2000), no. 4, 1073-1085.
    • (2000) Nonlinearity , vol.13 , Issue.4 , pp. 1073-1085
    • Ramani, A.1    Ohta, Y.2    Grammaticos, B.3
  • 35
    • 0342395256 scopus 로고
    • Level spacing distributions and the Bessel kernel
    • Tracy, C. A.; Widom, H. Level spacing distributions and the Bessel kernel. Comm. Math. Phys. 161 (1994), no. 2, 289-309.
    • (1994) Comm. Math. Phys. , vol.161 , Issue.2 , pp. 289-309
    • Tracy, C.A.1    Widom, H.2
  • 36
    • 0003025563 scopus 로고
    • Fredholm determinants, differential equations and matrix models
    • Tracy, C. A.; Widom, H. Fredholm determinants, differential equations and matrix models. Comm. Math. Phys. 163 (1994), no. 1, 33-72.
    • (1994) Comm. Math. Phys. , vol.163 , Issue.1 , pp. 33-72
    • Tracy, C.A.1    Widom, H.2
  • 37
    • 0030545965 scopus 로고    scopus 로고
    • On orthogonal and symplectic matrix ensembles
    • Tracy, C. A.; Widom, H. On orthogonal and symplectic matrix ensembles. Comm. Math. Phys. 177 (1996), no. 3, 727-754.
    • (1996) Comm. Math. Phys. , vol.177 , Issue.3 , pp. 727-754
    • Tracy, C.A.1    Widom, H.2
  • 38
    • 0033474974 scopus 로고    scopus 로고
    • Random unitary matrices, permutations and Painlevé
    • Tracy, C. A.; Widom, H. Random unitary matrices, permutations and Painlevé. Comm. Math. Phys. 207 (1999), no. 3, 665-685.
    • (1999) Comm. Math. Phys. , vol.207 , Issue.3 , pp. 665-685
    • Tracy, C.A.1    Widom, H.2
  • 39
    • 0035634442 scopus 로고    scopus 로고
    • On the distributions of the lengths of the longest monotone subsequences in random words
    • Tracy, C. A.; Widom, H. On the distributions of the lengths of the longest monotone subsequences in random words. Probab. Theory Related Fields 119 (2001), no. 3, 350-380.
    • (2001) Probab. Theory Related Fields , vol.119 , Issue.3 , pp. 350-380
    • Tracy, C.A.1    Widom, H.2
  • 40
    • 0141960836 scopus 로고    scopus 로고
    • Defining variety and birational canonical transformations of the fifth Painlevé equation
    • Watanabe, H. Defining variety and birational canonical transformations of the fifth Painlevé equation. Analysis (Munich) 18 (1998), no. 4, 351-357.
    • (1998) Analysis (Munich) , vol.18 , Issue.4 , pp. 351-357
    • Watanabe, H.1
  • 42
    • 0034258106 scopus 로고    scopus 로고
    • Gap probabilities for edge intervals in finite Gaussian and Jacobi unitary matrix ensembles
    • Witte, N. S.; Forrester, P. J.; Cosgrove, C. M. Gap probabilities for edge intervals in finite Gaussian and Jacobi unitary matrix ensembles. Nonlinearity 13 (2000), no. 5, 1439-1464.
    • (2000) Nonlinearity , vol.13 , Issue.5 , pp. 1439-1464
    • Witte, N.S.1    Forrester, P.J.2    Cosgrove, C.M.3


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