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Volumn 115, Issue 3-4, 2004, Pages 749-803

Fluctuations of the one-dimensional polynuclear growth model in half-space

Author keywords

Airy process; KPZ universality class; Polynuclear growth; Random matrices; Tracy Widom distribution

Indexed keywords


EID: 3543005380     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/b:joss.0000022374.73462.85     Document Type: Article
Times cited : (87)

References (51)
  • 3
    • 4243979739 scopus 로고
    • Dynamic scaling of growing interfaces
    • M. Kardar, G. Parisi, and Y. C. Zhang, Dynamic scaling of growing interfaces, Phys. Rev. Lett. 56:889-892 (1986).
    • (1986) Phys. Rev. Lett. , vol.56 , pp. 889-892
    • Kardar, M.1    Parisi, G.2    Zhang, Y.C.3
  • 4
    • 11944258149 scopus 로고
    • Six-vertex model, roughened surfaces, and an asymmetric spin Hamiltonian
    • L.-H. Gwa and H. Spohn, Six-vertex model, roughened surfaces, and an asymmetric spin Hamiltonian, Phys. Rev. Lett. 68:725-728 (1992).
    • (1992) Phys. Rev. Lett. , vol.68 , pp. 725-728
    • Gwa, L.-H.1    Spohn, H.2
  • 5
    • 0001288820 scopus 로고
    • Bethe ansatz solution for crossover scaling functions of the asymmetric XXZ chain and the Kardar-Parisi-Zhang-type growth model
    • D. Kim, Bethe ansatz solution for crossover scaling functions of the asymmetric XXZ chain and the Kardar-Parisi-Zhang-type growth model, Phys. Rev. E 52:3512-3524 (1995).
    • (1995) Phys. Rev. E , vol.52 , pp. 3512-3524
    • Kim, D.1
  • 6
    • 0034340689 scopus 로고    scopus 로고
    • Shape fluctuations and random matrices
    • K. Johansson, Shape fluctuations and random matrices, Commun. Math. Phys. 209: 437-476 (2000).
    • (2000) Commun. Math. Phys. , vol.209 , pp. 437-476
    • Johansson, K.1
  • 7
    • 0000439075 scopus 로고    scopus 로고
    • Universal distributions for growth processes in 1 + 1 dimensions and random matrices
    • M. Prähofer and H. Spohn, Universal distributions for growth processes in 1 + 1 dimensions and random matrices, Phys. Rev. Lett 84:4882-4885 (2000).
    • (2000) Phys. Rev. Lett , vol.84 , pp. 4882-4885
    • Prähofer, M.1    Spohn, H.2
  • 8
    • 0343391145 scopus 로고    scopus 로고
    • Statistical self-similarity of one-dimensional growth processes
    • M. Prähofer and H. Spohn, Statistical self-similarity of one-dimensional growth processes, Physica A 279:342-352 (2000).
    • (2000) Physica A , vol.279 , pp. 342-352
    • Prähofer, M.1    Spohn, H.2
  • 9
    • 0034338413 scopus 로고    scopus 로고
    • Limiting distributions for a polynuclear growth model with external sources
    • J. Baik and E. M. Rains, Limiting distributions for a polynuclear growth model with external sources, J. Stat. Phys 100:523-541 (2000).
    • (2000) J. Stat. Phys. , vol.100 , pp. 523-541
    • Baik, J.1    Rains, E.M.2
  • 10
    • 0035534219 scopus 로고    scopus 로고
    • Limit theorems for height fluctuations in a class of discrete space and time growth models
    • J. Gravner, C. A. Tracy, and H. Widom, Limit theorems for height fluctuations in a class of discrete space and time growth models, J. Stat. Phys. 102:1085-1132 (2001).
    • (2001) J. Stat. Phys. , vol.102 , pp. 1085-1132
    • Gravner, J.1    Tracy, C.A.2    Widom, H.3
  • 11
    • 0036630772 scopus 로고    scopus 로고
    • A growth model in a random environment
    • J. Gravner, C. A. Tracy, and H. Widom, A growth model in a random environment, Ann. Probab. 30:1340-1369 (2002).
    • (2002) Ann. Probab. , vol.30 , pp. 1340-1369
    • Gravner, J.1    Tracy, C.A.2    Widom, H.3
  • 12
    • 0036025750 scopus 로고    scopus 로고
    • Fluctuations in the composite regime of a disordered growth model
    • J. Gravner, C. A. Tracy, and H. Widom, Fluctuations in the composite regime of a disordered growth model, Commun. Math. Phys. 229:433-458 (2002).
    • (2002) Commun. Math. Phys. , vol.229 , pp. 433-458
    • Gravner, J.1    Tracy, C.A.2    Widom, H.3
  • 13
    • 0012620162 scopus 로고    scopus 로고
    • Current fluctuations for the totally asymmetric simple exclusion process
    • V. Sidoravicius, ed., Progress in Probability
    • M. Prähofer and H. Spohn, Current fluctuations for the totally asymmetric simple exclusion process, in In and Out of Equilibrium, V. Sidoravicius, ed., Progress in Probability, Vol. 51 (2002), pp. 185-204.
    • (2002) In and Out of Equilibrium , vol.51 , pp. 185-204
    • Prähofer, M.1    Spohn, H.2
  • 14
    • 0141450340 scopus 로고    scopus 로고
    • Scale invariance of the PNG droplet and the Airy process
    • M. Prähofer and H. Spohn, Scale invariance of the PNG droplet and the Airy process, J. Stat. Phys. 108:1071-1106 (2002).
    • (2002) J. Stat. Phys. , vol.108 , pp. 1071-1106
    • Prähofer, M.1    Spohn, H.2
  • 16
    • 0033443150 scopus 로고    scopus 로고
    • On the distribution of the length of the longest increasing subsequence in a random permutation
    • J. Baik, P. A. Deift, and K. Johansson, On the distribution of the length of the longest increasing subsequence in a random permutation, J. Amer. Math. Soc. 12:1119-1178 (1999).
    • (1999) J. Amer. Math. Soc. , vol.12 , pp. 1119-1178
    • Baik, J.1    Deift, P.A.2    Johansson, K.3
  • 17
    • 0033458290 scopus 로고    scopus 로고
    • Longest increasing subsequences: From patience sorting to the Baik-Deift-Johansson theorem
    • D. Aldous and P. Diaconis, Longest increasing subsequences: From patience sorting to the Baik-Deift-Johansson theorem, Bull. Amer. Math. Soc. 36:413-432 (1999).
    • (1999) Bull. Amer. Math. Soc. , vol.36 , pp. 413-432
    • Aldous, D.1    Diaconis, P.2
  • 18
    • 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
  • 19
    • 0242592942 scopus 로고    scopus 로고
    • Discrete polynuclear growth and determinantal processes
    • K. Johansson, Discrete polynuclear growth and determinantal processes, Commun. Math. Phys. 242:277-329 (2003).
    • (2003) Commun. Math. Phys. , vol.242 , pp. 277-329
    • Johansson, K.1
  • 20
    • 27644532196 scopus 로고
    • Level-spacing distributions and the Airy kernel
    • C. A. Tracy and H. Widom, Level-spacing distributions and the Airy kernel, Commun. Math. Phys. 159:151-174 (1994).
    • (1994) Commun. Math. Phys. , vol.159 , pp. 151-174
    • Tracy, C.A.1    Widom, H.2
  • 22
    • 0030545965 scopus 로고    scopus 로고
    • On orthogonal and symplectic matrix ensembles
    • C. A. Tracy and H. Widom, On orthogonal and symplectic matrix ensembles, Commun. Math. Phys. 177:727-754 (1996).
    • (1996) Commun. Math. Phys. , vol.177 , pp. 727-754
    • Tracy, C.A.1    Widom, H.2
  • 23
    • 0010152218 scopus 로고    scopus 로고
    • Algebraic aspects of increasing subsequences
    • J. Baik and E. M. Rains, Algebraic aspects of increasing subsequences, Duke Math. J. 109:1-65 (2001).
    • (2001) Duke Math. J. , vol.109 , pp. 1-65
    • Baik, J.1    Rains, E.M.2
  • 24
    • 0010151103 scopus 로고    scopus 로고
    • The asymptotics of monotone subsequences of involutions
    • J. Baik and E. M. Rains, The asymptotics of monotone subsequences of involutions, Duke Math. J. 109:205-281 (2001).
    • (2001) Duke Math. J. , vol.109 , pp. 205-281
    • Baik, J.1    Rains, E.M.2
  • 25
    • 0010126887 scopus 로고    scopus 로고
    • Symmetrized random permutations
    • P. M. Bleher and A. R. Its, eds.
    • J. Baik and E. M. Rains, Symmetrized random permutations, in Random Matrix Models and Their Applications, P. M. Bleher and A. R. Its, eds. (2001), pp. 1-29.
    • (2001) Random Matrix Models and Their Applications , pp. 1-29
    • Baik, J.1    Rains, E.M.2
  • 26
    • 0041637573 scopus 로고
    • A Brownian-motion model for the eigenvalues of a random matrix
    • F. J. Dyson, A Brownian-motion model for the eigenvalues of a random matrix, J. Math. Phys 3:1191-1198 (1962).
    • (1962) J. Math. Phys. , vol.3 , pp. 1191-1198
    • Dyson, F.J.1
  • 27
    • 0035626398 scopus 로고    scopus 로고
    • Discrete orthogonal polynomial ensembles and the Plancherel measure
    • K. Johansson, Discrete orthogonal polynomial ensembles and the Plancherel measure, Ann. Math. 153:259-296 (2001).
    • (2001) Ann. Math. , vol.153 , pp. 259-296
    • Johansson, K.1
  • 28
    • 0033516823 scopus 로고    scopus 로고
    • Correlations for the orthogonal-unitary and symplectic transitions at the hard and soft edges
    • P. J. Forrester, T. Nagao, and G. Honner, Correlations for the orthogonal-unitary and symplectic transitions at the hard and soft edges, Nucl. Phys. B 553:601-643 (1999).
    • (1999) Nucl. Phys. B , vol.553 , pp. 601-643
    • Forrester, P.J.1    Nagao, T.2    Honner, G.3
  • 29
    • 33845907500 scopus 로고
    • On the vector representations of induced matroids
    • B. Lindström, On the vector representations of induced matroids, Bull. London Math. Soc. 5:85-90 (1973).
    • (1973) Bull. London Math. Soc. , vol.5 , pp. 85-90
    • Lindström, B.1
  • 30
    • 0000868570 scopus 로고
    • Binomial determinants, paths, and hook length formulae
    • I. Gessel and G. Viennot, Binomial determinants, paths, and hook length formulae, Adv. Math. 58:300-321 (1985).
    • (1985) Adv. Math. , vol.58 , pp. 300-321
    • Gessel, I.1    Viennot, G.2
  • 32
    • 0002777429 scopus 로고
    • Nonintersecting paths, pfaffians, and plane partitions
    • J. R. Stembridge, Nonintersecting paths, pfaffians, and plane partitions, Adv. Math. 83: 96-131 (1990).
    • (1990) Adv. Math. , vol.83 , pp. 96-131
    • Stembridge, J.R.1
  • 33
    • 84967260423 scopus 로고
    • Coincidence properties of birth and death processes
    • S. Karlin and L. McGregor, Coincidence properties of birth and death processes, Pacific J. 9:1109-1140 (1959).
    • (1959) Pacific J. , vol.9 , pp. 1109-1140
    • Karlin, S.1    McGregor, L.2
  • 34
    • 84972545947 scopus 로고
    • Coincidence probabilities
    • S. Karlin and L. McGregor, Coincidence probabilities, Pacific J. 9:1141-1164 (1959).
    • (1959) Pacific J. , vol.9 , pp. 1141-1164
    • Karlin, S.1    McGregor, L.2
  • 35
    • 0034377725 scopus 로고    scopus 로고
    • Random vicious walks and random matrices
    • J. Baik, Random vicious walks and random matrices, Comm. Pure Appl. Math. 53: 1385-1410 (2000).
    • (2000) Comm. Pure Appl. Math. , vol.53 , pp. 1385-1410
    • Baik, J.1
  • 36
    • 0000540882 scopus 로고    scopus 로고
    • Vicious random walkers and a discretization of Gaussian random matrix ensembles
    • T. Nagao and P. J. Forrester, Vicious random walkers and a discretization of Gaussian random matrix ensembles, Nucl. Phys. B 620:551-565 (2002).
    • (2002) Nucl. Phys. B , vol.620 , pp. 551-565
    • Nagao, T.1    Forrester, P.J.2
  • 37
    • 0037454805 scopus 로고    scopus 로고
    • Dynamical correlations among vicious random walkers
    • T. Nagao, M. Katori, and H. Tanemura, Dynamical correlations among vicious random walkers, Phys. Lett. A 307:29-35 (2003).
    • (2003) Phys. Lett. A , vol.307 , pp. 29-35
    • Nagao, T.1    Katori, M.2    Tanemura, H.3
  • 38
    • 0032163852 scopus 로고    scopus 로고
    • Correlation functions, cluster functions, and spacing distributions for random matrices
    • C. A. Tracy and H. Widom, Correlation functions, cluster functions, and spacing distributions for random matrices, J. Stat. Phys. 92:809-835 (1998).
    • (1998) J. Stat. Phys. , vol.92 , pp. 809-835
    • Tracy, C.A.1    Widom, H.2
  • 39
    • 0001395985 scopus 로고
    • On some multiple integrals involving determinants
    • N. G. de Bruijn, On some multiple integrals involving determinants, J. Indian Math. Soc. 19:133-151 (1955).
    • (1955) J. Indian Math. Soc. , vol.19 , pp. 133-151
    • De Bruijn, N.G.1
  • 41
    • 33645840905 scopus 로고
    • Non-equilibrium behavior of a many particle process: Density profile and local equilibria
    • H. Rost, Non-equilibrium behavior of a many particle process: Density profile and local equilibria, Z. Warsch. Verw. Gebiete 58:41-53 (1981).
    • (1981) Z. Warsch. Verw. Gebiete , vol.58 , pp. 41-53
    • Rost, H.1
  • 42
    • 84957346702 scopus 로고
    • Universal parametric correlations at the soft edge of spectrum of random matrix ensembles
    • A. M. S. Macêdo, Universal parametric correlations at the soft edge of spectrum of random matrix ensembles, Europhys. Lett. 26:641-646 (1994).
    • (1994) Europhys. Lett. , vol.26 , pp. 641-646
    • Macêdo, A.M.S.1
  • 43
    • 0042597355 scopus 로고    scopus 로고
    • Multilevel dynamical correlation functions for Dyson's Brownian motion model of random matrices
    • T. Nagao and P. J. Forrester, Multilevel dynamical correlation functions for Dyson's Brownian motion model of random matrices, Phys. Lett. A 247:42-46 (1998).
    • (1998) Phys. Lett. A , vol.247 , pp. 42-46
    • Nagao, T.1    Forrester, P.J.2
  • 44
    • 3042655531 scopus 로고    scopus 로고
    • System of differential equations for the Airy process
    • C. A. Tracy and H. Widom, System of differential equations for the Airy process, Electron. Comm. Probab. 8:93-98 (2003).
    • (2003) Electron. Comm. Probab. , vol.8 , pp. 93-98
    • Tracy, C.A.1    Widom, H.2
  • 48
    • 0000817750 scopus 로고
    • Correlation functions of random matrix ensembles related to classical orthogonal polynomials
    • T. Nagao and M. Wadati, Correlation functions of random matrix ensembles related to classical orthogonal polynomials, J. Phys. Soc. Japan 60:3298-3322 (1991).
    • (1991) J. Phys. Soc. Japan , vol.60 , pp. 3298-3322
    • Nagao, T.1    Wadati, M.2
  • 49
    • 0003085922 scopus 로고
    • Correlation functions of random matrix ensembles related to classical orthogonal polynomials II
    • T. Nagao and M. Wadati, Correlation functions of random matrix ensembles related to classical orthogonal polynomials II, J. Phys. Soc. Japan 61:78-88 (1992).
    • (1992) J. Phys. Soc. Japan , vol.61 , pp. 78-88
    • Nagao, T.1    Wadati, M.2
  • 50
    • 0010028379 scopus 로고
    • Correlation functions of random matrix ensembles related to classical orthogonal polynomials III
    • T. Nagao and M. Wadati, Correlation functions of random matrix ensembles related to classical orthogonal polynomials III, J. Phys. Soc. Japan 61:1910-1918 (1992).
    • (1992) J. Phys. Soc. Japan , vol.61 , pp. 1910-1918
    • Nagao, T.1    Wadati, M.2
  • 51
    • 0041970774 scopus 로고
    • Four correspondences between graphs and generalized Young tableaux
    • W. H. Burge, Four correspondences between graphs and generalized Young tableaux, J. Combin. Theory Ser. A 17:12-30 (1974).
    • (1974) J. Combin. Theory Ser. A , vol.17 , pp. 12-30
    • Burge, W.H.1


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