The Annals of Applied Probability

The motion of a second class particle for the tasep starting from a decreasing shock profile

Thomas Mountford and Hervé Guiol

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We prove a strong law of large numbers for the location of the second class particle in a totally asymmetric exclusion process when the process is started initially from a decreasing shock. This completes a study initiated in Ferrari and Kipnis [Ann. Inst. H. Poincaré Probab. Statist. 13 (1995) 143–154].

Article information

Ann. Appl. Probab., Volume 15, Number 2 (2005), 1227-1259.

First available in Project Euclid: 3 May 2005

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Zentralblatt MATH identifier

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 82C22: Interacting particle systems [See also 60K35]

Totally asymmetric exclusion second class particle rarefaction fan Seppäläinen’s variational formula concentration inequalities last passage percolation


Mountford, Thomas; Guiol, Hervé. The motion of a second class particle for the tasep starting from a decreasing shock profile. Ann. Appl. Probab. 15 (2005), no. 2, 1227--1259. doi:10.1214/105051605000000151.

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  • Dembo, A. and Zeitouni, O. (1998). Large Deviations Techniques and Applications, 2nd ed. Springer, New York.
  • Evans, L. C. (1998). Partial Differential Equations. Amer. Math. Soc., Providence, RI.
  • Ferrari, P. A. (1992). Shock fluctuations in asymmetric simple exclusion. Probab. Theory Related Fields 91 81–101.
  • Ferrari, P. A. and Kipnis, C. (1995). Second class particles in the rarefaction fan. Ann. Inst. H. Poincaré Probab. Statist. 31 143–154.
  • Ferrari, P. A., Kipnis, C. and Saada, E. (1991). Microscopic structure of travelling waves in the asymmetric simple exclusion process. Ann. Probab. 19 226–244.
  • Johansson, K. (2000). Shape fluctuations and random matrices. Comm. Math. Phys. 209 437–476.
  • Kesten, H. (1993). On the speed of convergence in first-passage percolation. Ann. Appl. Probab. 3 296–338.
  • Kipnis, C. and Landim, C. (1999). Scaling Limits of Interacting Particle Systems. Springer, Berlin.
  • Liggett, T. M. (1985). Interacting Particle Systems. Springer, New York.
  • Rezakhanlou, F. (1991). Hydrodynamic limit for attractive particle systems on $\Z^d$. Comm. Math. Phys. 140 417–448.
  • Rezakhanlou, F. (1995). Microscopic structure of shocks in one conservation laws. Ann. Inst. H. Poincaré Anal. Non Linéaire 12 119–153.
  • Rost, H. (1981). Nonequilibrium behaviour of a many particle process: Density profile and local equilibria. Z. Wahrsch. Verw. Gebiete 58 41–53.
  • Seppäläinen, T. (1998). Hydrodynamic scaling, convex duality and asymptotic shapes of growth models. Markov Process. Related Fields 4 1–26.
  • Seppäläinen, T. (1999). Existence of hydrodynamics for the totally asymmetric simple $K$-exclusion process. Ann. Probab. 27 361–415.
  • Seppäläinen, T. (2001). Hydrodynamic profiles for the totally asymmetric exclusion process with a slow bond. J. Statist. Phys. 102 69–96.
  • Seppäläinen, T. (2001). Second class particles as microscopic characteristics in totally asymmetric nearest-neighbor $K$-exclusion processes. Trans. Amer. Math. Soc. 353 4801–4829.