The KPZ fixed point for discrete time TASEPs
arXiv:2002.06824 · doi:10.1088/1751-8121/aba213
Abstract
We consider two versions of discrete time totally asymmetric simple exclusion processes (TASEPs) with geometric and Bernoulli random 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 Mateski, Quastel and Remenik and allows us to take the KPZ scaling limit. For both the discrete time geometric and Bernoulli TASEPs, we show that the distribution function converges to the one describing the KPZ fixed point.
31 pages, 1 figure. To appear in J. Phys. A
References in corpus (4)
- Fluctuation properties of the TASEP with periodic initial configuration
- Current Distribution and random matrix ensembles for an integrable asymmetric fragmentation process
- Dynamics of a tagged particle in the asymmetric exclusion process with the step initial condition
- Determinant solution for the Totally Asymmetric Exclusion Process with parallel update