TASEP fluctuations with soft-shock initial data

@article{Quastel2018TASEPFW,
  title={TASEP fluctuations with soft-shock initial data},
  author={J. Quastel and Mustazee Rahman},
  journal={arXiv: Probability},
  year={2018}
}
  • J. Quastel, Mustazee Rahman
  • Published 2018
  • Physics, Mathematics
  • arXiv: Probability
  • We consider the totally asymmetric simple exclusion process with \emph{soft-shock} initial particle density, which is a step function increasing in the direction of flow and the step size chosen small to admit KPZ scaling. The initial configuration is deterministic and the dynamics create a shock. We prove that the fluctuations of a particle at the macroscopic position of the shock converge to the maximum of two independent GOE Tracy-Widom random variables, which establishes a conjecture of… CONTINUE READING
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