组合四面体链中的Z形及相应的马尔可夫链
Zigzags in combinatorial tetrahedral chains and the associated Markov chain
摘要：
嵌在曲面中的图中的Z字形是指任意两个相邻边不同、有一个公共顶点且属于同一个面的循环边序列。我们研究随机构造的组合四面体链中的双标记。每个这样的链最多包含$3$之字形直至反向。主要结果是随机构建的四面体链精确包含$k\in\{1,2,3\}$的概率的极限，当其长度接近无穷大时，该概率反向。我们的关键工具是马尔可夫链，其状态是$z$ -monodromies的类型。
英文摘要：
Zigzags in graphs embedded in surfaces are cyclic sequences of edges whose any two consecutive edges are different, have a common vertex and belong to the same face. We investigate zigzags in randomly constructed combinatorial tetrahedral chains. Every such chain contains at most $3$ zigzags up to reversing. The main result is the limit of the probability that a randomly constructed tetrahedral chain contains precisely $k\in\{1,2,3\}$ zigzags up to reversing as its length approaches infinity. Our key tool is the Markov chain whose states are types of $z$-monodromies.
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