论文标题
限制周期性tasep的一分分配
Limiting one-point distribution of periodic TASEP
论文作者
论文摘要
空间周期性完全不对称的简单排除过程的单点分布的放松时间限制预计将是周期域中KPZ普遍性类别中模型的通用一个点分布。与无限线案例不同，限制一个点分布在非平整时间参数上非依赖。我们研究了该分布的几种特性，以定期步骤和平坦的初始条件。我们表明，分布从较小的时间限制中的tracy-widom分布变化为在较大的时间限制下的高斯分布，并且也有史以来获得右尾估计。此外，我们建立了与可集成微分方程的连接，例如KP方程，MKDV和非线性热方程的耦合系统以及KDV方程。
The relaxation time limit of the one-point distribution of the spatially periodic totally asymmetric simple exclusion process is expected to be the universal one point distribution for the models in the KPZ universality class in a periodic domain. Unlike the infinite line case, the limiting one point distribution depends non-trivially on the scaled time parameter. We study several properties of this distribution for the case of the periodic step and flat initial conditions. We show that the distribution changes from a Tracy-Widom distribution in the small time limit to the Gaussian distribution in the large time limit, and also obtain right tail estimate for all time. Furthermore, we establish a connection to integrable differential equations such as the KP equation, coupled systems of mKdV and nonlinear heat equations, and the KdV equation.
