标题： 非平稳广义TASEP在KPZ和阻塞区域 显示英文标题

标题： Nonstationary generalized TASEP in KPZ and jamming regimes

摘要： 我们研究了具有广义更新的完全不对称排除过程模型，与通常的完全不对称排除过程相比，该模型有一个额外的参数，增强了粒子的聚类。 我们推导了在两种初始条件（阶梯和交替一次）下，无限晶格上粒子行驶距离的精确多粒子分布。 研究了精确公式的两种不同的尺度极限。 在与Kardar-Parisi-Zhang（KPZ） universality class相关的第一个尺度下，我们证明了缩放后的粒子位置的联合分布收敛到通用的Airy$_2$和 Airy$_1$过程的有限维分布。 在第二个尺度下，我们证明了相同的位置分布收敛到两个新的随机过程的有限维分布，这些过程描述了KPZ区域和确定性聚集区域之间的转变，在确定性聚集区域中，粒子相互粘附形成一个巨大的集群，作为一个粒子移动。 结果显示，过渡分布在极限情况下包括Airy过程和完全相关的高斯波动。 我们还给出了启发式论证，解释了在KPZ区域的渐近分析中出现的非通用尺度常数如何与无限系统中平移不变稳态的性质相关，以及在过渡区域中模型的参数应该如何缩放。 显示英文摘要

摘要： We study the model of the totally asymmetric exclusion process with generalized update, which compared to the usual totally asymmetric exclusion process, has an additional parameter enhancing clustering of particles. We derive the exact multiparticle distributions of distances travelled by particles on the infinite lattice for two types of initial conditions: step and alternating once. Two different scaling limits of the exact formulas are studied. Under the first scaling associated to Kardar-Parisi-Zhang (KPZ) universality class we prove convergence of joint distributions of the scaled particle positions to finite-dimensional distributions of the universal Airy$_2$ and Airy$_1$ processes. Under the second scaling we prove convergence of the same position distributions to finite-dimensional distributions of two new random processes, which describe the transition between the KPZ regime and the deterministic aggregation regime, in which the particles stick together into a single giant cluster moving as one particle. It is shown that the transitional distributions have the Airy processes and fully correlated Gaussian fluctuations as limiting cases. We also give the heuristic arguments explaining how the non-universal scaling constants appearing from the asymptotic analysis in the KPZ regime are related to the properties of translationally invariant stationary states in the infinite system and how the parameters of the model should scale in the transitional regime.