We review a recent development at the interface between discrete mathematics on one hand and probability theory and statistics on the other, specifically the use of Markov chains and their boundary theory in connection with the asymptotics of randomly growing permutations. Permutations connect total orders on a finite set, which leads to the use of a pattern frequencies. This view is closely related to classical concepts of nonparametric statistics. We give several applications and discuss related topics and research areas, in particular the treatment of other combinatorial families, the cycle view of permutations, and an approach via exchangeability.

翻译：我们审视了离散数学与概率理论和统计数据之间的界面方面的最新动态,特别是Markov链条及其边界理论在随机增长变异的无症状作用方面的使用情况。变相将一定系列的总订单连接在一起,从而导致使用一个模式频率。这种观点与非参数统计的经典概念密切相关。我们给出了几种应用,并讨论了相关专题和研究领域,特别是其他组合家庭的处理、周期性变异观点以及通过互换方式的方法。