论文标题
离散时间周期性TASEP的多点分布
Multi-point distribution of discrete time periodic TASEP
论文作者
论文摘要
我们研究了一维离散时间完全不对称的简单排除过程，并在空间周期性域上具有并行更新规则。对于一般初始条件，获得了多点时空联合分布公式。该公式涉及与某些离散空间作用的内核的弗雷霍尔姆决定因素的轮廓积分。对于满足某些技术假设的一类初始条件，在放松时间尺度下，当高度波动受到有限的几何形状严重影响时，我们能够在宽松时间尺度$ t = o（l^{3/2}）$中得出大型，大周期的限制。对于步骤和平坦的初始条件，对假设进行了验证。作为推论，我们通过将$ l $足够大的$ \ mathbb {z} $在整个整数晶格$ \ mathbb {z} $上获得多点分布，以使有限的时间分布不受边界的影响。然后，对于步骤初始条件，获得了$ \ mathbb {z} $上离散时间TASEP的多时间分配的较大时间限制。
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.
