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arXiv · 0907.0226

Limit process of stationary TASEP near the characteristic line

Jinho Baik·Patrik L. Ferrari·Sandrine Péché
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Abstract

The totally asymmetric simple exclusion process (TASEP) on Z with the Bernoulli-rho measure as initial conditions, 0<rho<1, is stationary. It is known that along the characteristic line, the current fluctuates as of order t^{1/3}. The limiting distribution has also been obtained explicitly. In this paper we determine the limiting multi-point distribution of the current fluctuations moving away from the characteristics by the order t^{2/3}. The main tool is the analysis of a related directed last percolation model. We also discuss the process limit in tandem queues in equilibrium.

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Jinho Baik, Patrik L. Ferrari, Sandrine Péché. 2012-10-26. Limit process of stationary TASEP near the characteristic line. https://doi.org/10.1002/cpa.20316

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