论文标题
在广义对称组上随机步行：单面转置洗牌的截止
Random Walks on the Generalized Symmetric Group: Cutoff for the One-sided Transposition Shuffle
论文作者
论文摘要
在本文中，我们提供了一个详细的证明，以展示广义对称组$ g_ {m，n} $上的单方面转座（OST）随机的截止。我们的工作表明，基于$ M \ leq 2 $ Matheau-Raven证明的技术，我们可以证明对任何固定的$ g_ {m，n} $在任何固定的$ g_ {m，n} $上的无偏见的截止距离，任何固定的$ m \ geq geq geq geq geq 1 $ in Time $ n \ log（n）$。我们还证明了$ g_ {m，n} $的简单模块的分支规则，并为证明$ g_ {m，n} $的任何一般有偏见的OST Shuffle的总变化距离证明了临界值的猜想的一些数学基础。
In this paper, we present a detailed proof for the exhibition of a cutoff for the one-sided transposition (OST) shuffle on the generalized symmetric group $G_{m,n}$. Our work shows that based on techniques for $m \leq 2$ proven by Matheau-Raven, we can prove the cutoff in total variation distance and separation distance for an unbiased OST shuffle on $G_{m,n}$ for any fixed $m \geq 1$ in time $n \log(n)$. We also prove the branching rules for the simple modules of $G_{m,n}$ and lay down some of the mathematical foundation for proving the conjecture for the cutoff in total variation distance for any general biased OST shuffle on $G_{m,n}$.
