Finite Time Corrections in KPZ Growth Models

Journal of Statistical Physics

Volumn 144, Issue 6, 2011, Pages 1123-1150

  Ferrari, Patrik L ^a   Frings, René ^a  

^a UNIVERSITY OF BONN   (Germany)

Author keywords

Finite size; Growth models; KPZ class; Universality

Indexed keywords

EID: 80052931563     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-011-0318-4     Document Type: Article

References (43)

1. Abramowitz, M., Stegun, I. A.: Pocketbook of Mathematical Functions. Verlag Harri Deutsch, Thun-Frankfurt am Main (1984).
2. Amir, G., Corwin, I., Quastel, J.: Probability distribution of the free energy of the continuum directed random polymer in 1+1 dimensions. Commun. Pure Appl. Math. 64, 466-537 (2011).
3. Baik, J., Deift, P. A., Johansson, K.: On the distribution of the length of the longest increasing subsequence of random permutations. J. Am. Math. Soc. 12, 1119-1178 (1999).
4. Baik, J., Rains, E. M.: Limiting distributions for a polynuclear growth model with external sources. J. Stat. Phys. 100, 523-542 (2000).
5. Baik, J., Rains, E. M.: Algebraic aspects of increasing subsequences. Duke Math. J. 109, 1-65 (2001).
6. Bertini, L., Giacomin, G.: Stochastic Burgers and KPZ equations from particle system. Commun. Math. Phys. 183, 571-607 (1997).
7. Bornemann, F.: On the numerical evaluation of Fredholm determinants. Math. Comput. 79, 871-915 (2009).
8. Borodin, A., Ferrari, P. L.: Anisotropic growth of random surfaces in 2+1 dimensions. arXiv: 0804. 3035 (2008).
9. Borodin, A., Ferrari, P. L.: Large time asymptotics of growth models on space-like paths I: PushASEP. Electron. J. Probab. 13, 1380-1418 (2008).
10. Borodin, A., Ferrari, P. L., Prähofer, M., Sasamoto, T.: Fluctuation properties of the TASEP with periodic initial configuration. J. Stat. Phys. 129, 1055-1080 (2007).
11. Borodin, A., Ferrari, P. L., Sasamoto, T.: Large time asymptotics of growth models on space-like paths II: PNG and parallel TASEP. Commun. Math. Phys. 283, 417-449 (2008).
12. Calabrese, P., Le Doussal, P., Rosso, A.: Free-energy distribution of the directed polymer at high temperature. Europhys. Lett. 90, 20002 (2010).
13. Choup, L. N.: Edgeworth expansion of the largest eigenvalue distribution function of GUE and LUE. Int. Math. Res. Not. 2006 (2006).
14. Dotsenko, V.: Replica Bethe ansatz derivation of the Tracy-Widom distribution of the free energy fluctuations in one-dimensional directed polymers. J. Stat. Mech., P07010 (2010).
15. Ferrari, P. L.: Polynuclear growth on a flat substrate and edge scaling of GOE eigenvalues. Commun. Math. Phys. 252, 77-109 (2004).
16. Ferrari, P. L.: From interacting particle systems to random matrices. J. Stat. Mech., P10016 (2010).
17. Ferrari, P. L., Prähofer, M.: One-dimensional stochastic growth and Gaussian ensembles of random matrices. Markov Process. Relat. Fields 12, 203-234 (2006).
18. Ferrari, P. L., Spohn, H.: Random growth models. arXiv: 1003. 0881 (2010).
19. Johansson, K.: Shape fluctuations and random matrices. Commun. Math. Phys. 209, 437-476 (2000).
20. Johansson, K.: Discrete polynuclear growth and determinantal processes. Commun. Math. Phys. 242, 277-329 (2003).
21. Kardar, K., Parisi, G., Zhang, Y. Z.: Dynamic scaling of growing interfaces. Phys. Rev. Lett. 56, 889-892 (1986).
22. El Karoui, N.: A rate of convergence result for the largest eigenvalue of complex white Wishart matrices. Ann. Probab. 34, 2077-2117 (2006).
23. Koekoek, R., Swarttouw, R. F.: The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue. arXiv: math. CA/9602214 (1996).
24. Maunuksela, J., Myllys, M., Kähkönen, O.-P., Timonen, J., Provatas, N., Alava, M. J., Ala-Nissila, T.: Kinetic roughening in slow combustion of paper. Phys. Rev. Lett. 79, 1515-1518 (1997).
25. Okounkov, A.: Infinite wedge and random partitions. Sel. Math. 7, 57-81 (2001).
26. Prähofer, M., Spohn, H.: Universal distributions for growth processes in 1+1 dimensions and random matrices. Phys. Rev. Lett. 84, 4882-4885 (2000).
27. Prähofer, M., Spohn, H.: Scale invariance of the PNG droplet and the Airy process. J. Stat. Phys. 108, 1071-1106 (2002).
28. Prolhac, S., Spohn, H.: The one-dimensional KPZ equation and the Airy process. J. Stat. Mech., P03020 (2011).
29. Richter, M.: Finite size corrections in the polynuclear growth model via numerical Fredholm determinants. Diploma thesis, University of Bonn (2011).
30. Sasamoto, T.: Spatial correlations of the 1D KPZ surface on a flat substrate. J. Phys. A 38, 549-556 (2005).
31. Sasamoto, T., Spohn, H.: Exact height distributions for the KPZ equation with narrow wedge initial condition. Nucl. Phys. B 834, 523-542 (2010).
32. Sasamoto, T., Spohn, H.: One-dimensional Kardar-Parisi-Zhang equation: an exact solution and its universality. Phys. Rev. Lett. 104, 230602 (2010).
33. Sasamoto, T., Spohn, H.: The 1+1-dimensional Kardar-Parisi-Zhang equation and its universality class. J. Stat. Mech., P11013 (2010).
34. Sasamoto, T., Spohn, H.: The crossover regime for the weakly asymmetric simple exclusion process. J. Stat. Phys. 140, 209-231 (2010).
35. Takeuchi, K., Sano, M.: Growing interfaces of liquid crystal turbulence: universal scaling and fluctuations. Phys. Rev. Lett. 104, 230601 (2010).
36. Takeuchi, K., Sano, M., Sasamoto, T., Spohn, H.: Growing interfaces uncover universal fluctuations behind scale invariance. Sci. Rep. 34 (2011).
37. Tracy, C. A., Widom, H.: Level-spacing distributions and the Airy kernel. Commun. Math. Phys. 159, 151-174 (1994).
38. Tracy, C. A., Widom, H.: On orthogonal and symplectic matrix ensembles. Commun. Math. Phys. 177, 727-754 (1996).
39. Tracy, C. A., Widom, H.: A Fredholm determinant representation in ASEP. J. Stat. Phys. 132, 291-300 (2008).
40. Tracy, C. A., Widom, H.: Integral formulas for the asymmetric simple exclusion process. Commun. Math. Phys. 279, 815-844 (2008).
41. Tracy, C. A., Widom, H.: Asymptotics in ASEP with step initial condition. Commun. Math. Phys. 290, 129-154 (2009).
42. Tracy, C. A., Widom, H.: Total current fluctuations in ASEP. J. Math. Phys. 50, 095204 (2009).
43. Wakita, J., Itoh, H., Matsuyama, T., Matsushita, M.: Self-affinity for the growing interface of bacterial colonies. J. Phys. Soc. Jpn. 66, 67-72 (1997).