Anomalous shock fluctuations in TASEP and last passage percolation models
arXiv:1306.3336 · doi:10.1007/s00440-013-0544-6
Abstract
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.
51 pages, 7 figures; Results for TASEP and LPP extended and better illustrated
References in corpus (5)
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Cited by in corpus (12)
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- Stationary half-space last passage percolation
- Shock fluctuations in flat TASEP under critical scaling
- Finite GUE distribution with cut-off at a shock
- Statistics of TASEP with three merging characteristics
- TASEP fluctuations with soft-shock initial data
- Coupling derivation of optimal-order central moment bounds in exponential last-passage percolation
- TASEP with a general initial condition and a deterministically moving wall
- Hydrodynamic limit for a 2D interlaced particle process
- The stochastic six-vertex model speed process
- The second class particle in the half-line open TASEP