Convergence of exclusion processes and the KPZ equation to the KPZ fixed point

@article{Quastel2020ConvergenceOE,
  title={Convergence of exclusion processes and the KPZ equation to the KPZ fixed point},
  author={Jeremy Quastel and Sourav Sarkar},
  journal={arXiv: Probability},
  year={2020}
}
We show that under the 1:2:3 scaling, critically probing large space and time, the height function of finite range asymmetric exclusion processes and the KPZ equation converge to the KPZ fixed point, constructed earlier as a limit of the totally asymmetric simple exclusion process through exact formulas. Consequently, based on recent results of \cite{wu},\cite{DM20}, the KPZ line ensemble converges to the Airy line ensemble. For the KPZ equation we are able to start from a continuous function… 

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