随机仿射外尔群元的形状与随机核划分
The shape of a random affine Weyl group element and random core partitions
摘要：
设$W$是有限外尔群，${\hat{W}}$是相应的仿射外尔群.我们表明，一个大的元素在${\hat{W}}$，随机产生的（减少）乘简单的发电机，几乎肯定有一个$|W|$特定的形状。等价地，在仿射Coxeter排列的区域中的约化的随机游动渐近地接近$|W|$ -许多方向中的一个。该方向的坐标以及每个方向的概率可以通过$W$上的马尔可夫链来计算。我们的结果，适用于类型$\tilde{A}_{n-1}$，表明一个大的随机$n$ -核心从自然增长过程中获得的限制形状是一个分段线性图。在这种情况下，我们的随机过程是TASEP的周期模拟，我们的极限形状可以与Rost定理TASEP的极限形状进行比较。
英文摘要：
Let $W$ be a finite Weyl group and ${\hat{W}}$ be the corresponding affine Weyl group. We show that a large element in ${\hat{W}}$, randomly generated by (reduced) multiplication by simple generators, almost surely has one of $|W|$-specific shapes. Equivalently, a reduced random walk in the regions of the affine Coxeter arrangement asymptotically approaches one of $|W|$-many directions. The coordinates of this direction, together with the probabilities of each direction can be calculated via a Markov chain on $W$. Our results, applied to type $\tilde{A}_{n-1}$, show that a large random $n$-core obtained from the natural growth process has a limiting shape which is a piecewise-linear graph. In this case, our random process is a periodic analogue of TASEP, and our limiting shapes can be compared with Rost's theorem on the limiting shape of TASEP.
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