论文标题
置换统计的极端价值
Extreme Values of Permutation Statistics
论文作者
论文摘要
我们研究了由有限的Coxeter组的随机元素的计数和下降产生的Mahonian和Eulerian分布的极端值。为此，我们构建了一个分布的三角形阵列，这些阵列的分布是从等级增加的一系列Coxeter组中。为了避免极值的退化，I.I.D的数量每行的样本$ k_n $必须渐近地界定。我们采用大型偏差理论来证明Mahonian和Eulerian分布的吸引力。结果表明，对于这两个类别，$ k_n $的不同界限可确保这一点。
We investigate extreme values of Mahonian and Eulerian distributions arising from counting inversions and descents of random elements of finite Coxeter groups. To this end, we construct a triangular array of either distribution from a sequence of Coxeter groups with increasing ranks. To avoid degeneracy of extreme values, the number of i.i.d. samples $k_n$ in each row must be asymptotically bounded. We employ large deviations theory to prove the Gumbel attraction of Mahonian and Eulerian distributions. It is shown that for the two classes, different bounds on $k_n$ ensure this.
