Two speed TASEP

Journal of Statistical Physics

Volumn 137, Issue 5, 2009, Pages 936-977

  Borodin, Alexei ^a   Ferrari, Patrik L ^b   Sasamoto, Tomohiro ^c,d  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^b UNIVERSITY OF BONN   (Germany)

^c CHIBA UNIVERSITY   (Japan)

^d TECHNICAL UNIVERSITY OF MUNICH   (Germany)

Author keywords

Airy processes; Random matrices; Shock fluctuations; TASEP

Indexed keywords

EID: 74449093118     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-009-9837-7     Document Type: Article

References (39)

1. Adler, M., Ferrari, P. L., van Moerbeke, P.: Airy processes with wanderers and new universality classes. arXiv: 0811. 1863. Ann. Probab. (2008, to appear).
2. Baik, J., Ben Arous, G., Péché, S.: Phase transition of the largest eigenvalue for non-null complex sample covariance matrices. Ann. Probab. 33, 1643-1697 (2006).
3. Borodin, A., Ferrari, P. L.: Anisotropic growth of random surfaces in 2+1 dimensions. arXiv: 0804. 3035 (2008).
4. Borodin, A., Ferrari, P. L.: Large time asymptotics of growth models on space-like paths I: PushASEP. Electron. J. Probab. 13, 1380-1418 (2008).
5. Borodin, A., Ferrari, P. L., Prähofer, M.: Fluctuations in the discrete TASEP with periodic initial configurations and the Airy1 process. Int. Math. Res. Papers 2007, rpm002 (2007).
6. 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).
7. Borodin, A., Ferrari, P. L., Prähofer, M., Sasamoto, T., Warren, J.: Maximum of Dyson Brownian motion and non-colliding systems with a boundary. arXiv: 0905. 3989 (2009).
8. Borodin, A., Ferrari, P. L., Sasamoto, T.: Transition between Airy1 and Airy2 processes and TASEP fluctuations. Commun. Pure Appl. Math. 61, 1603-1629 (2008).
9. Borodin, A., Kuan, J.: Random surface growth with a wall and Plancherel measures for O(∞). arXiv: 0904. 2607 (2009).
10. Borodin, A., Péché, S.: Airy kernel with two sets of parameters in directed percolation and random matrix theory. J. Stat. Phys. 132, 275-290 (2008).
11. Burke, P. J.: The output of a queuing system. Oper. Res. 4, 699-704 (1956).
12. Coletti, C. F., Ferrari, P. A., Pimentel, L. P. R.: The variance of the shock in the HAD process. arXiv: 0801. 2526 (2008).
13. Derrida, B., Gerschenfeld, A.: Current fluctuations of the one dimensional symmetric exclusion process with a step initial condition. J. Stat. Phys. 136, 1-15 (2009).
14. Defosseux, M.: Orbit measures and interlaced determinantal point processes. C. R. Math. Acad. Sci. Paris 346, 783-788 (2008).
15. Defosseux, M.: Orbit measures, random matrix theory and interlaced determinantal processes. arXiv: 0810. 1011 (2008).
16. Derrida, B., Janowsky, S. A., Lebowitz, J. L., Speer, E. R.: Exact solution of the totally asymmetric simple exclusion process: shock profiles. J. Stat. Phys. 73, 813-842 (1993).
17. Ferrari, P. A.: Shock fluctuations in asymmetric simple exclusion. Probab. Theory Relat. Fields 91, 81-101 (1992).
18. Ferrari, P. L.: The universal Airy1 and Airy2 processes in the totally asymmetric simple exclusion process. In: Baik, J., et al. (eds.) Integrable Systems and Random Matrices: In Honor of Percy Deift. Contemporary Math., pp. 321-332. American Mathematics Society, Providence (2008).
19. Ferrari, P. L.: Java animation of the TASEP with one slow particle. http://www-wt. iam. uni-bonn. de/~ferrari/animations/TASEPAnimation. html.
20. Ferrari, P. L., Prähofer, M.: One-dimensional stochastic growth and Gaussian ensembles of random matrices. Markov Processes Relat. Fields 12, 203-234 (2006) (Proceedings of "Inhomogeneous Random Systems 2005").
21. Ferrari, P. L., Spohn, H.: A determinantal formula for the GOE Tracy-Widom distribution. J. Phys. A 38, L557-L561 (2005).
22. Forrester, P. J., Nordenstam, E.: The anti-symmetric GUE Minor Process. arXiv: 0804. 3293 (2008).
23. Imamura, T., Sasamoto, T.: Dynamical properties of a tagged particle in the totally asymmetric simple exclusion process with the step-type initial condition. J. Stat. Phys. 128, 799-846 (2007).
24. Johansson, K.: Non-intersecting, simple, symmetric random walks and the extended Hahn kernel. Ann. Inst. Fourier 55, 2129-2145 (2005).
25. Katori, M., Tanemura, H.: Symmetry of matrix-valued stochastic processes and noncolliding diffusion particle systems. J. Math. Phys. 45, 3058-3085 (2004).
26. Katori, M., Tanemura, H.: Infinite systems of noncolliding generalized meanders and Riemann-Liouville differintegrals. Probab. Theory Relat. Fields 138, 113-156 (2007).
27. Koekoek, R., Swarttouw, R. F.: The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue. arXiv: math. CA/9602214.
28. Prähofer, M., Spohn, H.: Current fluctuations for the totally asymmetric simple exclusion process. In: Sidoravicius, V. (ed.) In and Out of Equilibrium. Progress in Probability, vol. 51, pp. 185-204. Birkhäuser, Boston (2002).
29. d. Commun. Math. Phys. 140, 417-448 (1991).
30. Sasamoto, T.: Spatial correlations of the 1D KPZ surface on a flat substrate. J. Phys. A 38, L549-L556 (2005).
31. Sasamoto, T.: Fluctuations of the one-dimensional asymmetric exclusion process using random matrix techniques, J. Stat. Mech., P07007 (2007).
32. Spohn, H.: Exact solutions for KPZ-type growth processes, random matrices, and equilibrium shapes of crystals. Physica A 369, 71-99 (2006).
33. Spohn, H.: Large Scale Dynamics of Interacting Particles, Texts and Monographs in Physics. Springer, Heidelberg (1991).
34. Tracy, C. A., Widom, H.: On orthogonal and symplectic matrix ensembles. Commun. Math. Phys. 177, 727-754 (1996).
35. Tracy, C. A., Widom, H.: Nonintersecting Brownian excursions. Ann. Appl. Probab. 17, 953-979 (2007).
36. Tracy, C. A., Widom, H.: Integral formulas for the asymmetric simple exclusion process. Commun. Math. Phys. 279, 815-844 (2008).
37. Tracy, C. A., Widom, H.: Asymptotics in ASEP with step initial condition. Commun. Math. Phys. 290, 129-154 (2009).
38. Warren, J., Windridge, P.: Some examples of dynamics for Gelfand Tsetlin patterns. Electron. J. Probab. 14, 1745-1769 (2009).
39. Whitham, G. B.: Linear and Nonlinear Waves. Wiley, New York (1999).