Fluctuations of the one-dimensional polynuclear growth model with external sources

Nuclear Physics B

Volumn 699, Issue 3, 2004, Pages 503-544

  Imamura, T ^a   Sasamoto, T ^b  

^a UNIVERSITY OF TOKYO   (Japan)

^b TOKYO INSTITUTE OF TECHNOLOGY   (Japan)

Author keywords

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

Indexed keywords

EID: 4844224385     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nuclphysb.2004.07.030     Document Type: Article

References (36)

1. P. Meakin Fractals, Scaling and Growth Far From Equilibrium 1998 Cambridge Univ. Press Cambridge
2. M. Kardar G. Parisi Y.C. Zhang Dynamic scaling of growing interfaces Phys. Rev. Lett. 56 1986 889-892
3. L.-H. Gwa H. Spohn Six-vertex model, roughened surfaces, and an asymmetric spin Hamiltonian Phys. Rev. Lett. 68 1992 725-728
4. 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 1995 3512-3524
5. C.A. Tracy H. Widom Level-spacing distributions and the Airy kernel Commun. Math. Phys. 159 1994 151-174
6. C.A. Tracy H. Widom On orthogonal and symplectic matrix ensembles Commun. Math. Phys. 177 1996 727-754
7. M.L. Mehta Random Matrices second ed. 1991 Academic Press San Diego, CA
8. K. Johansson Shape fluctuations and random matrices Commun. Math. Phys. 209 2000 437-476
9. M. Prähofer H. Spohn Current fluctuations for the totally asymmetric simple exclusion process in: V. Sidoravicius (Ed.) In and Out of Equilibrium in: Progress in Probability vol. 51 2002 Birkhäuser Basel 185-204
10. T. Nagao T. Sasamoto Asymmetric simple exclusion process and modified random matrix ensembles cond-mat/0405321
11. A. Rákos G.M. Schütz Current distribution and random matrix ensembles for an integrable asymmetric fragmentation process cond-mat/0405464
12. J. Gravner C.A. Tracy H. Widom Limit theorems for height fluctuations in a class of discrete space and time growth models J. Stat. Phys. 102 2001 1085-1132
13. S.N. Majumdar S. Nechaev An anisotropic ballistic deposition model with links to the Ulam problem and the Tracy - Widom distribution Phys. Rev. E 69 2004 011103
14. M. Prähofer H. Spohn Statistical self-similarity of one-dimensional growth processes Physica A 279 2000 342-352
15. J. Baik P.A. Deift K. Johansson On the distribution of the length of the longest increasing subsequence in a random permutation J. Amer. Math. Soc. 12 1999 1119-1178
16. J. Baik E.M. Rains Algebraic aspects of increasing subsequences Duke Math. J. 109 2001 1-65
17. J. Baik E.M. Rains The asymptotics of monotone subsequences of involutions Duke Math. J. 109 2001 205-281
18. J. Baik E.M. Rains Symmetrized random permutations in: P.M. Bleher A.R. Its (Eds.) Random Matrix Models and Their Applications 2001 Cambridge Univ. Press Cambridge 1-29
19. M. Prähofer H. Spohn Universal distributions for growth processes in 1 + 1 dimensions and random matrices Phys. Rev. Lett. 84 2000 4882-4885
20. P.L. Ferrari Polynuclear growth on a flat substrate and edge scaling of GOE eigenvalues math-ph/0402053
21. M. Prähofer H. Spohn Scale invariance of the PNG droplet and the Airy process J. Stat. Phys. 108 2002 1071-1106
22. K. Johansson Discrete polynuclear growth and determinantal processes Commun. Math. Phys. 242 2003 277-329
23. P.L. Ferrari H. Spohn Step fluctuations for a faceted crystal J. Stat. Phys. 113 2003 1-46
24. P.L. Ferrari M. Prähofer H. Spohn Fluctuations of an atomic ledge bordering a crystalline facet Phys. Rev. E 69 2004 035102
25. T. Sasamoto T. Imamura Fluctuations of the one-dimensional polynuclear growth model in half-space J. Stat. Phys. 115 2004 749-803
26. T. Nagao M. Katori H. Tanemura Dynamical correlations among vicious random walkers Phys. Lett. A 307 2003 29-35
27. J. Baik E.M. Rains Limiting distributions for a polynuclear growth model with external sources J. Stat. Phys. 100 2000 523-541
28. K. Johansson Non-intersecting paths, random tilings and random matrices Probab. Theory Related Fields 123 2002 225-280
29. F.J. Dyson A Brownian-motion model for the eigenvalues of a random matrix J. Math. Phys. 3 1962 1191-1198
30. P.J. Forrester T. Nagao G. Honner Correlations for the orthogonal - unitary and symplectic transitions at the hard and soft edges Nucl. Phys. B 553 1999 601-643
31. A.M.S. Macêdo Universal parametric correlations at the soft edge of spectrum of random matrix ensembles Europhys. Lett. 26 1994 641-646
32. P.J. Forrester Painlevé transcendent evaluation of the scaled distribution of the smallest eigenvalue in the Laguerre orthogonal and symplectic ensembles nlin.SI/0005064
33. M. Prähofer H. Spohn Exact scaling functions for one-dimensional stationary KPZ growth J. Stat. Phys. 115 2004 255-279
34. T. Imamura T. Sasamoto in preparation
35. C.A. Tracy H. Widom The distribution of the largest eigenvalue in the Gaussian ensembles: β = 1,2,4, in: J.F. van Diejen L. Vinet (Eds.) Calogero - Sutherland - Moser Models in: CRM Series in Mathematical Physics vol. 4 2000 Springer-Verlag New York 461-472
36. C.A. Tracy H. Widom Universality of the distribution functions of random matrix theory in: M.T. Batchelor L.T. Wille (Eds.) Statistical Physics on the Eve of the 21st Century: In Honor of J.B. McGuire on the Occasion of His 65th Birthday 1999 World Scientific Singapore 230-239