Generalizations of TASEP in Discrete and Continuous Inhomogeneous Space
Generalizations of TASEP in Discrete and Continuous Inhomogeneous Space
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DOI：
10.1007/s00220-019-03495-4
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发表时间：
2019-12-01
影响因子：
2.4
通讯作者：
Saenz, Axel
中科院分区：
文献类型：
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作者：
Knizel, Alisa;Petrov, Leonid;Saenz, Axel
我们研究了一类丰富的新的精确可解粒子系统，推广了完全不对称简单排斥过程(TASEP)。我们的粒子系统可以被认为是串联排队、有向第一或最后通过渗流模型或具有随机输入的Robinson-Schensted-Knuth类型系统的新的精确可解的例子。粒子系统的一个新特征是存在空间不均匀，这可能导致交通拥堵的形成。对于具有特殊阶跃初值的系统，我们找到了显式的极限形状，描述了流体动力学演化，得到了渐近涨落的结果，将系统归入Kardar-Parisi-Zhang普适类。在连续空间TASEP中交通拥堵的临界标度附近，我们观察到了Tracy-Widom分布和扩展的Ary核的形变，揭示了这种新型相变的更精细的结构。我们考虑的离散空间系统的齐次形式是几何末道渗流的单参数变形，我们得到了极限形状抛物线的推广和相应的渐近涨落结果。精确的可解性和渐近性态结果是由与Schur测度和过程的一个新的非平凡联系所赋予的。
We investigate a rich new class of exactly solvable particle systems generalizing the Totally Asymmetric Simple Exclusion Process (TASEP). Our particle systems can be thought of as new exactly solvable examples of tandem queues, directed first- or last-passage percolation models, or Robinson-Schensted-Knuth type systems with random input. One of the novel features of the particle systems is the presence of spatial inhomogeneity which can lead to the formation of traffic jams. For systems with special step-like initial data, we find explicit limit shapes, describe hydrodynamic evolution, and obtain asymptotic fluctuation results which put the systems into the Kardar-Parisi-Zhang universality class. At a critical scaling around a traffic jam in the continuous space TASEP, we observe deformations of the Tracy-Widom distribution and the extended Airy kernel, revealing the finer structure of this novel type of phase transitions. A homogeneous version of a discrete space system we consider is a one-parameter deformation of the geometric last-passage percolation, and we obtain extensions of the limit shape parabola and the corresponding asymptotic fluctuation results. The exact solvability and asymptotic behavior results are powered by a new nontrivial connection to Schur measures and processes.