메뉴 건너뛰기




Volumn 16, Issue 6, 2003, Pages

Growth models, random matrices and Painlevé transcendents

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0242679434     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/16/6/201     Document Type: Review
Times cited : (18)

References (40)
  • 2
    • 51249162954 scopus 로고
    • Hammersley's interacting particle process and longest increasing subsequences
    • Aldous D and Diaconis P 1995 Hammersley's interacting particle process and longest increasing subsequences Prob. Theory Rel. Fields 103 199-213
    • (1995) Prob. Theory Rel. Fields , vol.103 , pp. 199-213
    • Aldous, D.1    Diaconis, P.2
  • 3
    • 0033458290 scopus 로고    scopus 로고
    • Longest increasing subsequences: From patience sorting to, the Baik-Deift-Johansson theorem
    • Aldous D and Diaconis P 1999 Longest increasing subsequences: from patience sorting to, the Baik-Deift-Johansson theorem Bull. Am. Math. Soc. 36 413-32
    • (1999) Bull. Am. Math. Soc. , vol.36 , pp. 413-432
    • Aldous, D.1    Diaconis, P.2
  • 5
    • 0033443150 scopus 로고    scopus 로고
    • On the distribution of the length of the longest increasing subsequence of random permutations
    • Baik J, Deift P and Johansson K 1999 On the distribution of the length of the longest increasing subsequence of random permutations J. Am. Math. Soc. 12 1119-78
    • (1999) J. Am. Math. Soc. , vol.12 , pp. 1119-1178
    • Baik, J.1    Deift, P.2    Johansson, K.3
  • 6
    • 0034338413 scopus 로고    scopus 로고
    • Limiting distributions for a polynuclear growth model with external sources
    • Baik J and Rains E M 2000 Limiting distributions for a polynuclear growth model with external sources J. Stat. Phys. 100 523-41
    • (2000) J. Stat. Phys. , vol.100 , pp. 523-541
    • Baik, J.1    Rains, E.M.2
  • 7
    • 0010152218 scopus 로고    scopus 로고
    • Algebraic aspects of increasing subsequences
    • Baik J and Rains E M 2001 Algebraic aspects of increasing subsequences Duke Math. J. 109 1-65
    • (2001) Duke Math. J. , vol.109 , pp. 1-65
    • Baik, J.1    Rains, E.M.2
  • 8
    • 0010151103 scopus 로고    scopus 로고
    • The asymptotics of monotone subsequences of involutions
    • Baik J and Rains E M 2001 The asymptotics of monotone subsequences of involutions Duke Math. J. 109 205-81
    • (2001) Duke Math. J. , vol.109 , pp. 205-281
    • Baik, J.1    Rains, E.M.2
  • 10
    • 0038209546 scopus 로고    scopus 로고
    • Discrete gap probabilities and discrete Painlevé equations
    • Borodin A 2003 Discrete gap probabilities and discrete Painlevé equations Duke Math. J. 117 489-542
    • (2003) Duke Math. J. , vol.117 , pp. 489-542
    • Borodin, A.1
  • 11
    • 0037471252 scopus 로고    scopus 로고
    • Increasing subsequences and the hard-to-soft transition in matrix ensembles
    • Borodin A and Forrester P J 2003 Increasing subsequences and the hard-to-soft transition in matrix ensembles J. Phys. A: Math. Gen. 36 2963-81
    • (2003) J. Phys. A: Math. Gen. , vol.36 , pp. 2963-2981
    • Borodin, A.1    Forrester, P.J.2
  • 12
    • 34250142002 scopus 로고
    • Walks, walls, wetting and melting
    • Fisher M E 1984 Walks, walls, wetting and melting J. Stat. Phys. 34 667-729
    • (1984) J. Stat. Phys. , vol.34 , pp. 667-729
    • Fisher, M.E.1
  • 13
    • 0001657172 scopus 로고
    • Exact solution of the lockstep model of vicious walkers
    • Forrester P J 1990 Exact solution of the lockstep model of vicious walkers J. Phys. A: Math. Gen. 23 1259-73
    • (1990) J. Phys. A: Math. Gen. , vol.23 , pp. 1259-1273
    • Forrester, P.J.1
  • 14
    • 36449000028 scopus 로고
    • Exact results and universal asymptotics in the Laguerre random matrix ensemble
    • Forrester P J 1993 Exact results and universal asymptotics in the Laguerre random matrix ensemble J. Math. Phys. 35 2539-51
    • (1993) J. Math. Phys. , vol.35 , pp. 2539-2551
    • Forrester, P.J.1
  • 15
    • 0035839403 scopus 로고    scopus 로고
    • Random walks and random permutations
    • Forrester P J 2001 Random walks and random permutations J. Phys. A: Math. Gen. 34 L417-23
    • (2001) J. Phys. A: Math. Gen. , vol.34
    • Forrester, P.J.1
  • 19
    • 0042974080 scopus 로고    scopus 로고
    • τ-Function evaluations of gap probabilities in orthogonal and symplectic matrix ensembles
    • Forrester P J and Witte N S 2002 τ-Function evaluations of gap probabilities in orthogonal and symplectic matrix ensembles Nonlinearity 15 937-54
    • (2002) Nonlinearity , vol.15 , pp. 937-954
    • Forrester, P.J.1    Witte, N.S.2
  • 20
    • 0010198787 scopus 로고    scopus 로고
    • Application of the τ-function theory of Painlevé equations to random matrices: PVI, the JUE, CyUE, cJUE and scaled limits
    • in press (math-ph/0204008)
    • Forrester P J and Witte N S 2002 Application of the τ-function theory of Painlevé equations to random matrices: PVI, the JUE, CyUE, cJUE and scaled limits Nagoya Math. J. in press (math-ph/0204008)
    • (2002) Nagoya Math. J.
    • Forrester, P.J.1    Witte, N.S.2
  • 21
    • 0242708626 scopus 로고    scopus 로고
    • Discrete Painlevé equations and random matrix averages
    • Forrester P J and Witte N S 2003 Discrete Painlevé equations and random matrix averages Nonlinearity 16 1919-44
    • (2003) Nonlinearity , vol.16 , pp. 1919-1944
    • Forrester, P.J.1    Witte, N.S.2
  • 23
    • 0003166713 scopus 로고
    • Symmetric functions and p-recursiveness
    • Gessel I M 1990 Symmetric functions and p-recursiveness J. Comb. Theory A 53 257-85
    • (1990) J. Comb. Theory A , vol.53 , pp. 257-285
    • Gessel, I.M.1
  • 24
    • 0000203379 scopus 로고
    • An extension of Schensted's theorem
    • Greene C 1974 An extension of Schensted's theorem Adv. Math. 14 254-65
    • (1974) Adv. Math. , vol.14 , pp. 254-265
    • Greene, C.1
  • 25
    • 0012575045 scopus 로고
    • Kinetic roughening phenomena, stochastic growth, directed polymers and all that
    • Halpin-Healy T and Zhang Y C 1995 Kinetic roughening phenomena, stochastic growth, directed polymers and all that Phys. Rep. 254 215-415
    • (1995) Phys. Rep. , vol.254 , pp. 215-415
    • Halpin-Healy, T.1    Zhang, Y.C.2
  • 26
    • 0019147547 scopus 로고
    • A boundary value problem associated with the second Painlevé transcendent and the Korteweg-de Vries equation
    • Hastings S P and McLeod J B 1980 A boundary value problem associated with the second Painlevé transcendent and the Korteweg-de Vries equation Arch. Rat. Mech. Anal. 73 31-51
    • (1980) Arch. Rat. Mech. Anal. , vol.73 , pp. 31-51
    • Hastings, S.P.1    McLeod, J.B.2
  • 27
    • 0001292292 scopus 로고    scopus 로고
    • Unitary-matrix models and Painlevé III
    • Hisakado M 1996 Unitary-matrix models and Painlevé III Mod. Phys. Lett. A 11 3001-10
    • (1996) Mod. Phys. Lett. A , vol.11 , pp. 3001-3010
    • Hisakado, M.1
  • 28
    • 0037727538 scopus 로고    scopus 로고
    • Discriminants and functional equations for polynomials orthogonal on the unit circle
    • Ismail M E H and Witte N S 2001 Discriminants and functional equations for polynomials orthogonal on the unit circle J. Approx. Theory 110 200-28
    • (2001) J. Approx. Theory , vol.110 , pp. 200-228
    • Ismail, M.E.H.1    Witte, N.S.2
  • 29
    • 0034340689 scopus 로고    scopus 로고
    • Shape fluctuations and random matrices
    • Johansson K 2000 Shape fluctuations and random matrices Commun. Math. Phys. 209 437-76
    • (2000) Commun. Math. Phys. , vol.209 , pp. 437-476
    • Johansson, K.1
  • 30
    • 0036628218 scopus 로고    scopus 로고
    • Non-intersecting paths, random tilings and random matrices
    • Johansson K 2002 Non-intersecting paths, random tilings and random matrices Prob. Theory Rel. Fields 123 225-80
    • (2002) Prob. Theory Rel. Fields , vol.123 , pp. 225-280
    • Johansson, K.1
  • 31
    • 84972578253 scopus 로고
    • Permutations, matrices and generalized Young tableaux
    • Knuth D E 1970 Permutations, matrices and generalized Young tableaux Pacific J. Math. 34 709-27
    • (1970) Pacific J. Math. , vol.34 , pp. 709-727
    • Knuth, D.E.1
  • 32
    • 0347366076 scopus 로고
    • Unitary-matrix models as exactly solvable string theories
    • Periwal V and Shevitz D 1990 Unitary-matrix models as exactly solvable string theories Phys. Rev. Lett. 64 1326-9
    • (1990) Phys. Rev. Lett. , vol.64 , pp. 1326-1329
    • Periwal, V.1    Shevitz, D.2
  • 34
    • 10044262136 scopus 로고    scopus 로고
    • Increasing subsequences and the classical groups
    • Rains E M 1998 Increasing subsequences and the classical groups Elect. J. Combinatorics 5 #R12
    • (1998) Elect. J. Combinatorics , vol.5 , Issue.R12
    • Rains, E.M.1
  • 37
    • 27644532196 scopus 로고
    • Level-spacing distributions and the Airy kernel
    • Tracy C A and Widom H 1994 Level-spacing distributions and the Airy kernel Commun. Math. Phys. 159 151-74
    • (1994) Commun. Math. Phys. , vol.159 , pp. 151-174
    • Tracy, C.A.1    Widom, H.2
  • 38
    • 0030545965 scopus 로고    scopus 로고
    • On orthogonal and symplectic matrix ensembles
    • Tracy C A and Widom H 1996 On orthogonal and symplectic matrix ensembles Commun. Math. Phys. 177 727-54
    • (1996) Commun. Math. Phys. , vol.177 , pp. 727-754
    • Tracy, C.A.1    Widom, H.2
  • 39
    • 0033474974 scopus 로고    scopus 로고
    • Random unitary matrices, permutations and Painlevé
    • Tracy C A and Widom H 1999 Random unitary matrices, permutations and Painlevé Commun. Math. Phys. 207 665-85
    • (1999) Commun. Math. Phys. , vol.207 , pp. 665-685
    • Tracy, C.A.1    Widom, H.2
  • 40
    • 0013260919 scopus 로고
    • Une forme géométrique de la correspondance de Robinson-Schensted
    • Viennot G 1977 Une forme géométrique de la correspondance de Robinson-Schensted Lecture Notes in Math. 579 29-58
    • (1977) Lecture Notes in Math. , vol.579 , pp. 29-58
    • Viennot, G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.