标题： 有限版本的Toom模型 显示英文标题

标题： A finite variant of the Toom Model

摘要： 我们给出了具有闭边界的一维Toom模型的有限变体的结果。 我们证明稳态分布不是乘积形式，但仍然是简单的。 具体来说，我们给出了密度和一些最近邻关联函数的显式公式。 我们还通过与A. Schilling、B. Steinberg和N. M. Thiéry合作的${\mathscr R}$-平凡独异点理论，给出了转移矩阵的特征值和重数的精确结果。 显示英文摘要

摘要： We present results for a finite variant of the one-dimensional Toom model with closed boundaries. We show that the steady state distribution is not of product form, but is nonetheless simple. In particular, we give explicit formulas for the densities and some nearest neighbour correlation functions. We also give exact results for eigenvalues and multiplicities of the transition matrix using the theory of ${\mathscr R}$-trivial monoids in joint work with A. Schilling, B. Steinberg and N. M. Thi\'ery.