跳跃粒子的组合方法
A combinatorial approach to jumping particles
摘要：
本文考虑一个粒子在一排细胞上跳跃的模型，物理上称为一维完全非对称排它过程（TASEP）。更确切地说，我们处理的TASEP开放或周期边界条件和两种或三种类型的粒子。从组合学的观点来看，这个马尔可夫链的一个显著特征是，它在其平稳分布的几个条目中涉及Catalan数。我们给出了一个组合的解释和一个简单的证明这些意见。在这样做的时候，我们揭示了第二行细胞，粒子使用它来向后移动。作为一个副产品，我们还获得了布朗偏移的发生在一长排细胞上的粒子的密度的描述的解释。
英文摘要：
In this paper we consider a model of particles jumping on a row of cells, called in physics the one dimensional totally asymmetric exclusion process (TASEP). More precisely we deal with the TASEP with open or periodic boundary conditions and with two or three types of particles. From the point of view of combinatorics a remarkable feature of this Markov chain is that it involves Catalan numbers in several entries of its stationary distribution. We give a combinatorial interpretation and a simple proof of these observations. In doing this we reveal a second row of cells, which is used by particles to travel backward. As a byproduct we also obtain an interpretation of the occurrence of the Brownian excursion in the description of the density of particles on a long row of cells.
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