Multi-point distribution of discrete time periodic TASEP

Abstract

We study the one-dimensional discrete time totally asymmetric simple exclusion process with parallel update rules on a spatially periodic domain. A multi-point space-time joint distribution formula is obtained for general initial conditions. The formula involves contour integrals of Fredholm determinants with kernels acting on certain discrete spaces. For a class of initial conditions satisfying certain technical assumptions, we are able to derive large-time, large-period limit of the joint distribution, under the relaxation time scale $t=O(L^{3/2})$ when the height fluctuations are critically affected by the finite geometry. The assumptions are verified for the step and flat initial conditions. As a corollary we obtain the multi-point distribution of discrete time TASEP on the whole integer lattice $\mathbb{Z}$ by taking the period $L$ large enough so that the finite-time distribution is not affected by the boundary. The large time limit for multi-time distribution for discrete time TASEP on $\mathbb{Z}$ is then obtained for the step initial condition.

53 pages, 2 figures, minor modifications this version. arXiv admin note: text overlap with arXiv:1912.10143 by other authors

References in corpus (6)

• Asymptotics in ASEP with Step Initial Condition
• Fluctuation properties of the TASEP with periodic initial configuration
• The KPZ fixed point
• The directed landscape
• Determinant solution for the Totally Asymmetric Exclusion Process with parallel update
• Periodic TASEP with general initial conditions