论文标题
限制在经典仿期Weyl组中随机行走的方向
Limiting directions for random walks in classical affine Weyl groups
论文作者
论文摘要
令$ w $为有限的Weyl组，$ \ widetilde w $是相应的杂物韦尔组。 $ \ widetilde w $的随机元素可以作为在$ \ widetilde w $的壁co上进行的减少随机步行。通过Lam的定理（Ann。prob。2015），这样的步行几乎可以肯定接近了$ | w | $许多方向之一。当$ W $为$ b_n $，$ c_n $和$ d_n $时，我们计算这些说明，并且随机步行由KAC和Dual KAC标签加权。这解决了LAM在肯定的$ B $和$ c $的类型和$ c $的问题和$ d $中的问题。主要工具是一个组合两行模型，用于完全不对称的简单排除过程，称为$ d^*$ - tasep，带有四个参数。通过以不同的方式专业的参数，我们为上述每个Weyl组获得taseps。计算这些taseps中的某些相关性给出了所需的限制说明。
Let $W$ be a finite Weyl group and $\widetilde W$ the corresponding affine Weyl group. A random element of $\widetilde W$ can be obtained as a reduced random walk on the alcoves of $\widetilde W$. By a theorem of Lam (Ann. Prob. 2015), such a walk almost surely approaches one of $|W|$ many directions. We compute these directions when $W$ is $B_n$, $C_n$ and $D_n$ and the random walk is weighted by Kac and dual Kac labels. This settles Lam's questions for types $B$ and $C$ in the affirmative and for type $D$ in the negative. The main tool is a combinatorial two row model for a totally asymmetric simple exclusion process called the $D^*$-TASEP, with four parameters. By specializing the parameters in different ways, we obtain TASEPs for each of the Weyl groups mentioned above. Computing certain correlations in these TASEPs gives the desired limiting directions.
