Recently Johansson and Rahman obtained the limiting multitime distribution for the discrete polynuclear growth model (Johansson and Rahman (2019)), which is equivalent to a discrete TASEP model with step initial condition. In this paper, we obtain a finite time multipoint distribution formula of continuous TASEP with general initial conditions in the space-time plane. We evaluate the limit of this distribution function when the times go to infinity at the same speed for both step and flat initial conditions. These limiting distributions are expected to be universal for all the models in the Kardar–Parisi–Zhang universality class.
The author was supported by the University of Kansas Start Up Grant, the University of Kansas New Faculty General Research Fund, Simons Collaboration Grant No. 637861, and NSF grant DMS-1953687.
The author would like to thank Jinho Baik for the communications, and hosting the author’s recent visit to the University of Michigan where they had many useful discussions on this paper. The author also would like to thank the Integrable Probability Focused Research Group, funded by NSF Grants DMS-1664531, 1664617, 1664619, 1664650, for their organizations on various research activities in integral probability, and their support for the authors participation in these activities. Finally, the author would like to thank the anonymous referees for their constructive comments that improved the quality of this paper.
"Multipoint distribution of TASEP." Ann. Probab. 50 (4) 1255 - 1321, July 2022. https://doi.org/10.1214/21-AOP1557