The KPZ fixed point for discrete time TASEPs. (English) Zbl 1519.82064
Summary: We consider two versions of discrete time totally asymmetric simple exclusion processes (TASEPs) with geometric and Bernoulli hopping probabilities. For the process mixed with these and continuous time dynamics, we obtain a single Fredholm determinant representation for the joint distribution function of particle positions with arbitrary initial data. This formula is a generalization of the recent result by K. Matetski et al. [Acta Math. 227, No. 1, 115–203 (2021; Zbl 1505.82041)] and allows us to take the KPZ scaling limit. For both the discrete time geometric and Bernoulli TASEPs, we show that the distribution functions converge to the one describing the KPZ fixed point.
MSC:
| 82C22 | Interacting particle systems in time-dependent statistical mechanics |
| 82C23 | Exactly solvable dynamic models in time-dependent statistical mechanics |
| 60K35 | Interacting random processes; statistical mechanics type models; percolation theory |
| 60H15 | Stochastic partial differential equations (aspects of stochastic analysis) |
| 82C44 | Dynamics of disordered systems (random Ising systems, etc.) in time-dependent statistical mechanics |
| 60J65 | Brownian motion |
Citations:
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