论文标题
（1,2）和（2,1）在正线晶格上随机步行的切割点
Cutpoints of (1,2) and (2,1) random walks on the lattice of positive half line
论文作者
论文摘要
在本文中，我们研究（1,2）和（2,1）在正线晶格上的不同环境中随机步行。我们假设站点$ n $的过渡概率在渐近常数为$ n \ rightarrow \infty。$（1,2）随机步行中，我们得到了各种逃生概率的详尽渐近行为，并达到了步行的概率。这种观察结果和对持续分数和非负矩阵的产物的微妙分析使我们能够为（（1,2）和（2,1）随机步行的切割点数量提供标准，这概括了E.Csáki，A.Földes和P.Révész[J. [J. [J.] [J. [J.理论。概率。 23：624-638（2010）]和H.-M。王[马尔可夫处理相关。田野25：125-148（2019）]。对于近乎流动的随机步行，只要有无限的剪切点，我们还会研究$ [0，n]中切口数量的渐近数。
In this paper, we study (1,2) and (2,1) random walks in varying environments on the lattice of positive half line. We assume that the transition probabilities at site $n$ are asymptotically constants as $n\rightarrow\infty.$ For (1,2) random walk, we get some elaborate asymptotic behaviours of various escape probabilities and hitting probabilities of the walk. Such observations and some delicate analysis of continued fractions and the product of nonnegative matrices enable us to give criteria for finiteness of the number of cutpoints of both (1,2) and (2,1) random walks, which generalize E. Csáki, A. Földes and P. Révész [J. Theor. Probab. 23: 624-638 (2010)] and H.-M. Wang [Markov Processes Relat. Fields 25: 125-148 (2019)]. For near-recurrent random walks, whenever there are infinitely many cutpoints, we also study the asymptotics of the number of cutpoints in $[0,n].$
