论文标题
从对称群体到自身的随机耦合和射击
Stochastic Couplings and Bijections from the Symmetric Group to Itself
论文作者
论文摘要
受到Feller联轴器和中国餐厅流程所描述的随机过程的启发，我们创建了四个不同的界限，从集合$ [1] \ times [2] \ times \ times \ cdot \ times \ times [n] $到$ s_n $中的单词中。然后，我们将这些地图与它们的倒数构成，以获得六种bex to $ s_n \ to s_n $的象征。在此之后，我们研究了这些地图的固定点（$ 1 $循环）和较高的$ k $ cycles。我们完全表征了它们的某些特性，并从经验上显示了这些地图上较高的$ k $循环结构的复杂性。
Inspired by the Stochastic processes described by the Feller Coupling and Chinese Restaurant Processes, we create four different bijections from words in the set $[1]\times [2] \times\cdot \times[n]$ to $S_n$. We then compose these maps with their inverse to obtain a toal of six bijections $S_n \to S_n$. Following that, we investigate the fixed points ($1$-cycle) and higher $k$-cycles of these maps. We characterized some of their properties completely as well as empirically showing the complexity of the higher $k$-cycle structures for these maps.
