A combinatorial approach to jumping particles
A combinatorial approach to jumping particles
复制标题
跳跃粒子的组合方法
DOI：
10.1016/j.jcta.2004.09.006
复制
发表时间：
2004
期刊：
影响因子：
--
通讯作者：
G. Schaeffer
中科院分区：
文献类型：
--
作者：
E. Duchi;G. Schaeffer
本文考虑了一种粒子在一排细胞上跳跃的模型，在物理学中称为一维完全不对称排斥过程（TASEP）。更准确地说，我们用开放或周期边界条件和两种或三种类型的粒子来处理TASEP。从组合学的角度来看，这个马尔可夫链的一个显著特征是它在平稳分布的几个条目中包含加泰罗尼亚数。我们对这些观察结果给出一个组合解释和一个简单的证明。在这个过程中，我们揭示了第二排细胞，这是粒子用来向后移动的。作为一个副产品，我们还在描述一长排细胞上的粒子密度时得到了对布朗偏移发生的解释。
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.