Probability Theory and Related Fields

, Volume 161, Issue 1–2, pp 61–109 | Cite as

Anomalous shock fluctuations in TASEP and last passage percolation models

  • Patrik L. FerrariEmail author
  • Peter Nejjar


We consider the totally asymmetric simple exclusion process with initial conditions and/or jump rates such that shocks are generated. If the initial condition is deterministic, then the shock at time \(t\) will have a width of order \(t^{1/3}\). We determine the law of particle positions in the large time limit around the shock in a few models. In particular, we cover the case where at both sides of the shock the process of the particle positions is asymptotically described by the Airy\(_1\) process. The limiting distribution is a product of two distribution functions, which is a consequence of the fact that at the shock two characteristics merge and of the slow decorrelation along the characteristics. We show that the result generalizes to generic last passage percolation models.

Mathematics Subject Classification

60K35 82C22 



The authors would like to thank Alexei Borodin and Tomohiro Sasamoto for early discussions about the problem, and Herbert Spohn for valuable remarks. The work of P.L. Ferrari was supported by the German Research Foundation via the SFB 1060–B04 project. P. Nejjar is supported by the Bonn International Graduate School (BIGS).


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Institute for Applied MathematicsBonn UniversityBonnGermany

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