Abstract
We consider the totally asymmetric simple exclusion process (TASEP) with two different initial conditions with shock discontinuities formed by blocks of fully packed particles. Initially a second class particle is at the left of a shock discontinuity. Using multicolored TASEP we derive exact formulas for the distribution of the second class particle and colored height functions. These are given in terms of the height function at different positions of a single TASEP configuration. We study the limiting distributions of second class particles (and colored height functions). The result depends on how the width blocks of particles scale with the observation time; we study a variety of such scalings.
Funding Statement
The work of P. L. Ferrari is supported by the German Research Foundation through the Collaborative Research Center 1060 “The Mathematics of Emergent Effects” (Projekt ID 211504053), project B04. Furthermore, the work of both authors is supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy—GZ 2047/1, Projekt ID 390685813.
Acknowledgments
We are grateful to A. Borodin for very useful duscussions on the early stages of the project.
Citation
Alexey Bufetov. Patrik L. Ferrari. "Shock fluctuations in TASEP under a variety of time scalings." Ann. Appl. Probab. 32 (5) 3614 - 3644, October 2022. https://doi.org/10.1214/21-AAP1769
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