TASEP and generalizations: method for exact solution
TASEP and generalizations: method for exact solution
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DOI：
10.1007/s00440-022-01129-w
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发表时间：
2021-07
影响因子：
2
通讯作者：
K. Matetski;Daniel Remenik
中科院分区：
文献类型：
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作者：
K. Matetski;Daniel Remenik
在连续时间TASEP中发展的显式双正交化方法被推广到描述KPZ普适性类中几个相互作用的粒子系统的广泛的行列式度量。该方法被应用于具有行列式转移概率的离散时间TASEP的四个变体(具有Bernoulli和几何跳跃以及块和推送动态)中的每一个的顺序和并行更新版本；应用于连续时间PushASEP；以及具有广义更新的TASEP的一个版本。在所有情况下，多点分布函数都表示为具有显式核的Fredholm型行列式，该核涉及某些随机游动到由系统初始数据定义的曲线的命中时间。该方法进一步应用于交互毛虫系统，这是离散时间TASEP模型的扩展，该模型推广了顺序更新和并行更新。
The explicit biorthogonalization method, developed in for continuous time TASEP, is generalized to a broad class of determinantal measures which describe the evolution of several interacting particle systems in the KPZ universality class. The method is applied to sequential and parallel update versions of each of the four variants of discrete time TASEP (with Bernoulli and geometric jumps, and with block and push dynamics) which have determinantal transition probabilities; to continuous time PushASEP; and to a version of TASEP with generalized update. In all cases, multipoint distribution functions are expressed in terms of a Fredholm determinant with an explicit kernel involving hitting times of certain random walks to a curve defined by the initial data of the system. The method is further applied tosystems of interacting caterpillars, an extension of the discrete time TASEP models which generalizes sequential and parallel updates.