Journal of Statistical Physics

, Volume 160, Issue 4, pp 985–1004 | Cite as

Shock Fluctuations in Flat TASEP Under Critical Scaling

  • Patrik L. FerrariEmail author
  • Peter Nejjar


We consider TASEP with two types of particles starting at every second site. Particles to the left of the origin have jump rate \(1\), while particles to the right have jump rate \(\alpha \). When \(\alpha <1\) there is a formation of a shock where the density jumps to \((1-\alpha )/2\). For \(\alpha <1\) fixed, the statistics of the associated height functions around the shock is asymptotically (as time \(t\rightarrow \infty \)) a maximum of two independent random variables as shown in Ferrari and Nejjar (Probab Theory Rel Fields 161:61–109, 2015). In this paper we consider the critical scaling when \(1-\alpha =a t^{-1/3}\), where \(t\gg 1\) is the observation time. In that case the decoupling does not occur anymore. We determine the limiting distributions of the shock and numerically study its convergence as a function of \(a\). We see that the convergence to \(F_\mathrm{GOE}^2\) occurs quite rapidly as \(a\) increases. The critical scaling is analogue to the one used in the last passage percolation to obtain the BBP transition processes (Baik et al. in Ann Probab 33:1643–1697, 2006).


KPZ universality class Exclusion process Random matrices Shock fluctuations 



P. L. Ferrari was supported by the German Research Foundation via the SFB 1060-B04 Project. P. Nejjar is grateful for the support of the Bonn International Graduate School (BIGS).


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© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Institute for Applied MathematicsBonn UniversityBonnGermany

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