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 involves contour integrals of Fredholm determinants kernels acting certain spaces. For class conditions satisfying technical assumptions, we are able to derive large-time, large-period limit distribution, under relaxation scale $$t=O(L^{3/2})$$ t = O ( L 3 / 2 ) when height fluctuations critically affected by finite geometry. assumptions verified step and flat As corollary obtain TASEP whole integer lattice $${\mathbb {Z}}$$ Z taking period L large enough so that finite-time not boundary. multi-time then condition.