The crossover regime for the weakly asymmetric simple exclusion process

Journal of Statistical Physics

Volumn 140, Issue 2, 2010, Pages 209-231

  Sasamoto, Tomohiro ^a   Spohn, Herbert ^b  

^a CHIBA UNIVERSITY   (Japan)

^b TECHNICAL UNIVERSITY OF MUNICH   (Germany)

Author keywords

Finite time correction to Tracy Widom; KPZ crossover scale; WASEP

Indexed keywords

EID: 77954032129     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-010-9990-z     Document Type: Article

References (20)

1. Johansson, K.: Shape fluctuations and random matrices. Commun. Math. Phys. 209, 437-476 (2000).
2. Forrester, P. J.: The spectrum edge of random matrix ensembles. Nucl. Phys. B 402, 709-728 (1993).
3. Tracy, C. A., Widom, H.: Level-spacing distributions and the Airy kernel. Commun. Math. Phys. 159, 151-174 (1994).
4. Tracy, C. A., Widom, H.: Asymptotics in ASEP with step initial condition. Commun. Math. Phys. 290, 129-154 (2009).
5. Tracy, C. A., Widom, H.: Total current fluctuations in the asymmetric simple exclusion model. J. Math. Phys. 50, 095204 (2009).
6. Derrida, B., Gerschenfeld, A.: Current fluctuations of the one dimensional symmetric simple exclusion process with step initial condition. J. Stat. Phys. 136, 1-15 (2009).
7. Bertini, L., Giacomin, G.: Stochastic Burgers and KPZ equations from particle systems. Commun. Math. Phys. 183, 571-607 (1997).
8. De Masi, A., Presutti, E., Scacciatelli, E.: The weakly asymmetric exclusion process. Ann. Inst. Henri Poincaré, Probab. Stat. 25, 1-38 (1989).
9. Dittrich, P., Gärtner, J.: A central limit theorem for the weakly asymmetric simple exclusion process. Math. Nachr. 151, 75-93 (1991).
10. Spohn, H.: Large Scale Dynamics of Interacting Particles. Springer, Heidelberg (1991).
11. Kim, D.: Bethe ansatz for crossover scaling function of the asymmetric XXZ chain and the Kardar-Parisi-Zhang-type growth model. Phys. Rev. E 52, 3512-3524 (2000).
12. Derrida, B., Mallick, K.: Exact diffusion constant for the one-dimensional partially asymmetric exclusion model. J. Phys. A 30, 1031-1046 (1997).
13. Prolhac, S., Mallick, K.: Cumulants of the current in the weakly asymmetric exclusion process. J. Phys. A 42, 175001 (2009).
14. Balázs, M., Quastel, J., Seppäläinen, T.: Scaling exponent for the Cole-Hopf solution of the KPZ/stochastic Burgers. arXiv: 0909. 4816.
15. Sasamoto, T., Spohn, H.: Exact height distributions for the KPZ equation with narrow wedge initial condition. Nuclear Phys. B (2010). doi: 10. 1016. nuclphysb. 2010. 026.
16. Sasamoto, T., Spohn, H.: Universality of the one-dimensional KPZ equation. Preprint (2010). arXiv: 1002. 1883.
17. Andrews, G., Askey, R., Roy, R.: Special Functions. Cambridge University Press, Cambridge (1999).
18. Amir, G., Corwin, I., Quastel, J.: Probability Distribution of the free energy of the continuum directed random polymer in 1+1 dimensions. Preprint (2010). arXiv: 1003. 0443.
19. Reed, M., Simon, B.: Methods of Modern Mathematical Physics, vol. I. Academic Press, New York (1972).
20. Reed, M., Simon, B.: Methods of Modern Mathematical Physics, vol. IV. Academic Press, New York (1978).